Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

Hello,

I have updated to maple 2024 on both my desktop and my laptop, and now I am missing the feature "Convert Output Units:" in the context tab on my windows 11 laptop. It's still available on my windows 10 desktop.

I have tried reinstalling maple and installing java, but it unfortunately did not help. Due to limited school licences, I am unable to test with maple 2023.

Is this an issue you have heard of?

Thank you in advance,

Daniel

 

And here is the context menu on windows 11. Also nothing happens when I click "Format -> Convert Output Units" in the top menu. 

 

Hello, i have been drawing some cool 3d plots for my assignment, but when i use the export button and export it as pdf the plots turn out very low quality. 

See the image below is using the export function

Then i tried something different i tried using the print button and printing to a pdf.

That resulted in a different looking plot

This plot using the print to pdf feature looks much nicer, but the 3d text plot has become impossible to read.

 

Is there a way to fix that? Or to make the export to pdf feature export at higher quality? 

Best Regards

the second ode is giving me zero also when we back to orginal under the condition by using them must the orginal ode be zero but i don't know where is mistake , when Orginal paper use some thing different but i think they must have same results i don't know i use them wrong i am not sure at here just , when U(xi)=y(z) in my mw

restart

with(PDEtools)

NULL

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

NULL

G := V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

(2)

NULL

p := 2*k

2*k

(3)

ode := I*(-(diff(U(xi), xi))*p*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

(4)

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = (2/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/n^2, eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = (1/9)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/n^2, A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

(5)

n := 1

1

(6)

G := U(xi) = (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n)

U(xi) = 1/(B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))

(7)

pde3 := eval(ode, case1)

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+(k^2*B[1]^2-w*B[1]^2-1)*U(xi)*exp(I*(k*x-t*w))/B[1]^2+6*RootOf(3*_Z^2-3*_Z-1)*U(xi)^2*exp(I*(k*x-t*w))/B[1]-12*RootOf(3*_Z^2-3*_Z-1)*U(xi)^3*exp(I*(k*x-t*w))+(10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*U(xi)^4*exp(I*(k*x-t*w))+(1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*U(xi)^5*exp(I*(k*x-t*w)) = 0

(8)

odetest(eval(G, case1), pde3)

79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))

(9)

simplify(-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1)))

(((244512*B[1]^2-366768)*exp(10*xi)+(205920*B[1]^2+609984)*exp(12*xi)+(-7200*B[1]^2-394416)*exp(14*xi)+42480*exp(8*xi)*B[1]^2-27000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2-9504*exp(4*xi)*B[1]^2+48672*exp(6*xi)*B[1]^2+72*B[1]^2+144720*exp(8*xi)+55080*exp(16*xi)-18576*exp(2*xi)-20736*exp(4*xi)-8208*exp(6*xi)-1080)*RootOf(3*_Z^2-3*_Z-1)+(-79584*B[1]^2+479376)*exp(10*xi)+(-121440*B[1]^2-777888)*exp(12*xi)+(50400*B[1]^2+492912)*exp(14*xi)+127440*exp(8*xi)*B[1]^2+39000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2+1056*exp(4*xi)*B[1]^2-16608*exp(6*xi)*B[1]^2+24*B[1]^2-138240*exp(8*xi)-70560*exp(16*xi)-4752*exp(2*xi)-8352*exp(4*xi)+27792*exp(6*xi)-288)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(-3125*exp(20*xi)-25000*exp(18*xi)-76875*exp(16*xi)-108000*exp(14*xi)-55650*exp(12*xi)+12432*exp(10*xi)+11130*exp(8*xi)-4320*exp(6*xi)+615*exp(4*xi)-40*exp(2*xi)+1))

(10)

Download ode.mw

this is my first time something like that   coming up my equation after taking integral exponential coming up why?

g1.mw

Do you think the result of String(0.016)  should be "0.016"  instead of ".16e-1" ?

Any reason why it gives the second form and not the first?  Now have to keep using sprintf to force formating as decimal point. Is this documented somewhere? quick search did not find anything do far.

Maple 2024.2 on windows.

s:="0.016";

"0.016"

z:= :-parse(s);

0.16e-1

String(z);

".16e-1"

sprintf("%0.3f",z);

"0.016"

 

 

Download string_of_decimal_number.mw

The modified Liouville equation

How to solve this pde for a general solution ?

The general solution in this form exist.

restart;

with(PDEtools): declare(u(x,t)); U:=diff_table(u(x,t));
PDE1:=U[t,t]=a^2*U[x,x]+b*exp(beta*U[]);
Sol11:=u(x,t)=1/beta*ln(2*(B^2-a^2*A^2)/(b*beta*(A*x+B*t+C)^2));
Sol12:=S->u(x,t)=1/beta*ln(8*a^2*C/(b*beta))
-2/beta*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C);
Test11:=pdetest(Sol11,PDE1);
Test12:=pdetest(Sol12(1),PDE1);
Test13:=pdetest(Sol12(-1),PDE1);

u(x, t)*`will now be displayed as`*u

 

table( [(  ) = u(x, t) ] )

 

diff(diff(u(x, t), t), t) = a^2*(diff(diff(u(x, t), x), x))+b*exp(beta*u(x, t))

 

u(x, t) = ln(2*(-A^2*a^2+B^2)/(b*beta*(A*x+B*t+C)^2))/beta

 

proc (S) options operator, arrow; u(x, t) = ln(8*a^2*C/(b*beta))/beta-2*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C)/beta end proc

 

0

 

0

 

0

(1)

The Soll11 can be plotted with a Explore plot in this form of soll11 with th eparameters , but suppose i try to get the general solution in Maple ?

infolevel[pdsolve] := 3

pdsolve(PDE1, generalsolution)

ans := pdsolve(PDE1);

What solvin gstrategy to follow ? : the pde is a non-linear wave eqation  with a exponentiel sourceterm
It seems that the pde can reduced to a ode? :

 

with(PDEtools):
declare(u(x,t));

# Stap 1: Definieer de PDE
PDE := diff(u(x,t), t,t) = a^2 * diff(u(x,t), x,x) + b * exp(beta * u(x,t));

# Stap 2: Definieer de transformatie naar karakteristieke variabelen
# Nieuw: x en t uitgedrukt in ξ en η
tr := {
    x = (xi + eta)/2,
    t = (eta - xi)/(2*a)
};

# Pas de transformatie toe op de PDE
simplified_PDE := dchange(tr, PDE, [xi, eta], params = [a, b, beta], simplify);

# Stap 3: Definieer de algemene oplossing
solution := u(x,t) = (1/beta) * ln(
    (-8*a^2/(b*beta)) *
    diff(_F1(x - a*t), x) * diff(_F2(x + a*t), x) /
    (_F1(x - a*t) + _F2(x + a*t))^2
);

# Stap 4: Controleer de oplossing (optioneel)
pdetest(solution, PDE);  # Moet 0 teruggeven als correct

u(x, t)*`will now be displayed as`*u

 

diff(diff(u(x, t), t), t) = a^2*(diff(diff(u(x, t), x), x))+b*exp(beta*u(x, t))

 

{t = (1/2)*(eta-xi)/a, x = (1/2)*xi+(1/2)*eta}

 

a^2*(diff(diff(u(xi, eta), xi), xi)-2*(diff(diff(u(xi, eta), eta), xi))+diff(diff(u(xi, eta), eta), eta)) = a^2*(diff(diff(u(xi, eta), xi), xi))+2*a^2*(diff(diff(u(xi, eta), eta), xi))+a^2*(diff(diff(u(xi, eta), eta), eta))+b*exp(beta*u(xi, eta))

 

u(x, t) = ln(-8*a^2*(D(_F1))(-a*t+x)*(D(_F2))(a*t+x)/(b*beta*(_F1(-a*t+x)+_F2(a*t+x))^2))/beta

 

0

(2)

missing some steps here : solution u  without  the pde reduced ?
there is a ode ?

# Definieer de ODE # vorige stappen ontbreken van de reduktie
ode := (v^2 - a^2) * diff(f(xi), xi, xi) = b * exp(beta * f(xi));

# Algemene oplossing zoeken
sol := dsolve(ode, f(xi));

(-a^2+v^2)*(diff(diff(f(xi), xi), xi)) = b*exp(beta*f(xi))

 

f(xi) = ln((1/2)*c__1*(tan((1/2)*(-c__1*a^2*beta+c__1*beta*v^2)^(1/2)*(c__2+xi)/(a^2-v^2))^2+1)/b)/beta

(3)

 

, ,

Question : how do i arrive on Soll11   in Maple  ?

 

Download liouville_reduced_2-2-2025_mprimes_vraag.mw

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

(2)

pde := diff(u(x, y, z, t), `$`(t, 2))+diff(u(x, y, z, t), `$`(x, 2))-(diff(u(x, y, z, t)^2, `$`(x, 2)))-(diff(u(x, y, z, t), `$`(x, 4)))+diff(diff(u(x, y, z, t), y)+diff(u(x, y, z, t), z)+diff(u(x, y, z, t), t), x)+2*(diff(u(x, y, z, t), y, t))+diff(u(x, y, z, t), `$`(y, 2)) = 0

diff(diff(u(x, y, z, t), t), t)+diff(diff(u(x, y, z, t), x), x)-2*(diff(u(x, y, z, t), x))^2-2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))-(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))+diff(diff(u(x, y, z, t), x), y)+diff(diff(u(x, y, z, t), x), z)+diff(diff(u(x, y, z, t), t), x)+2*(diff(diff(u(x, y, z, t), t), y))+diff(diff(u(x, y, z, t), y), y) = 0

(3)

declare(v(t))

v(t)*`will now be displayed as`*v

(4)

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

(5)

Q := u(x, y, z, t) = 6*(diff(ln(f(x, y, z, t)), `$`(x, 2)))

LL := diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

(6)

S22 := f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)

f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)

(7)

NULL

R11 := eval(LL, S22)

k[1]^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*(k[1]+k[2])^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))^2*k[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*(k[1]+k[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-2*(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*s[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(s[1]+s[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]*l[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]*l[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])*(l[1]+l[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t) = 0

(8)

L4 := collect(%, [x, y, t], 'distributed')

k[1]^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*(k[1]+k[2])^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))^2*k[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*(k[1]+k[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-2*(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*s[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(s[1]+s[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]*l[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]*l[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])*(l[1]+l[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t) = 0

(9)

indets(%)

{t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2), (4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2), exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)}

(10)

eq2 := algsubs(exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z) = X, L4)

-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])*k[2]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^2*s[1]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^2*s[2]+5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^4*k[2]+10*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^3*k[2]^2+10*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*k[2]^3+5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]^4-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*s[1]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*s[2]-(9/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[2]^2*k[1]-(9/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[1]^2*k[2]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])*k[1]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])*k[2]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])*k[1]+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^5+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^5-(3/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[1]^3-(3/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[2]^3-(1/4)*k[1]*X*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])-(1/4)*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])-k[1]^2*s[1]*X-(3/4)*k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+k[1]^5*X-(3/4)*k[1]^3*X-2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]*s[1]-2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]*s[2]-(1/2)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2)*k[1]-(1/2)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2)*k[2] = 0

(11)

eq3 := simplify(eq2)

-(1/2)*(k[1]+k[2])*B[1]*((k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-8*k[1]*k[2]^3-12*k[2]^2*k[1]^2+(-8*k[1]^3+3*k[1]+2*s[1])*k[2]+2*s[2]*k[1])*exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = 0

(12)

indets(eq3)

{t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2), exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2]))}

(13)

eq4 := algsubs(exp((1/2)*t*sqrt(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))+(1/2)*t*sqrt(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = V, eq3)

-(1/2)*(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])*V = 0

(14)

indets(eq4)

{V, B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

(15)

eqs := {coeffs(collect(numer(normal(lhs(eq4))), {V}, 'distributed'), {V})}; nops(%); indets(eqs)

{-(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])}

 

1

 

{B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

(16)

vars := indets(eqs); ans := solve(eqs, vars)

{B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

 

Warning, solving for expressions other than names or functions is not recommended.

 

{B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = 0, k[1] = k[1], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = B[1], k[1] = k[1], k[2] = k[2], s[1] = (1/2)*(8*k[2]*k[1]^3+12*k[2]^2*k[1]^2+8*k[1]*k[2]^3-3*k[1]*k[2]-2*s[2]*k[1]-(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))/k[2], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

(17)

case2 := ans[1]

{B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

(18)

FF := subs(case2, S22)

NULL

F11 := eval(Q, FF)

pdetest(F11, pde)

-6*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(B[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+56*k[2]^4*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-6*k[2]^2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+B[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-24*B[1]*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+4*k[2]*s[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-4*k[2]*s[2]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*k[2]*s[2]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-224*k[2]^4*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-4*k[2]*s[2]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*k[2]*s[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+6*B[1]*k[2]^2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-8*B[1]*k[2]^4*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+3*B[1]*k[2]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-28*B[1]*k[2]^4*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-28*B[1]*k[2]^4*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+24*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+16*B[1]*k[2]*s[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-16*B[1]*k[2]*s[2]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+8*B[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-4*B[1]*k[2]*s[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]*k[2]*s[2]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-2*B[1]*k[2]*s[1]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*B[1]*k[2]*s[2]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*k[2]*s[1]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[2]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*k[2]*s[1]*B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[2]*B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[2]*B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*k[2]*s[1]*B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-4*B[1]*k[2]*s[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*B[1]*k[2]*s[2]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-2*B[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-2*B[1]*k[2]*s[2]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+32*B[1]*k[2]^4*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*k[2]*s[2]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-2*k[2]*s[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+3*k[2]^2*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+3*k[2]^2*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-28*k[2]^4*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-28*k[2]^4*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+3*B[1]*k[2]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-3*B[1]*k[2]^2*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]*k[2]^4*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*k[2]*s[2]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-B[1]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-B[1]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+4*B[1]*k[2]^4*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]^2*k[2]^4*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+16*k[2]*s[2]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-16*k[2]*s[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-8*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-6*k[2]^2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+56*k[2]^4*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+6*B[1]*k[2]^2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-8*B[1]*k[2]^4*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-3*B[1]*k[2]^2*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-3*B[1]^2*k[2]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-3*B[1]^2*k[2]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*B[1]^2*k[2]^4*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)))/(B[1]*exp(k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+exp(t*l[1]+2*k[2]*x+l[2]*y+s[2]*z-(1/2)*t*k[2]+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+exp(t*l[2]+l[1]*y+s[1]*z+(1/2)*t*k[2]+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+exp(t*l[1]+t*l[2]+x*k[2]))^4

(19)
 

NULL

Download hard_parameters.mw

in a lot of my equation i have such problem and really i don't know how fix this also i try to put : in end and sometime is work and i keep contionues  but sometime not there is any way for solve this problem?

limit.mw

It's 2024 and this is still something that doesn't exist? I'd just like to swap the Enter/Shfit+Enter behaviors since I find myself writing a lot of multi-line and custom procs and boy howdy it'd be nice if I could make Maple behave at least the littllest bit like, I dunno, every other product I own and use.

i found solution of PDE but there is some different from my solution and paper solution so there is must be a mistake becuase he solved by maple too he mentioned in the paper i try to figure out but i can't see any mistake from my solution can anyone watch where i did mistake, i change some letter in finding parameter but they are same like p=k&h=A&n=p&w=n

here is paper solution 

parameter-different.mw

I want to calculate Hodge Star of forms on a solvable Lie algebra L, I have defined a metric tensor g on it. But when I use that g to compute the Hodge Star of an operator it tells me that the g is not a metric tensor.

with(DifferentialGeometry);
with(LieAlgebras);
A := Matrix(4, 4, [[A__11, A__12, A__13, A__14], [A__21, -A__11, A__23, A__24], [-A__24, -A__23, -A__11, A__21], [-A__14, -A__13, A__12, A__11]]);
x := [x__1, x__2, x__3, x__4, x__5, x__6];
StructureEquations := [[x[6], x[1]] = a*x[1], [x[6], x[2]] = add(A[1, i]*x[i + 1], i = 1 .. 4), [x[6], x[3]] = add(A[2, i]*x[i + 1], i = 1 .. 4), [x[6], x[4]] = add(A[3, i]*x[i + 1], i = 1 .. 4), [x[6], x[5]] = add(A[4, i]*x[i + 1], i = 1 .. 4)];
L := LieAlgebraData(StructureEquations, [x[1], x[2], x[3], x[4], x[5], x[6]], Alg1);
DGsetup(L);
with(Tensor);
e := [e1, e2, e3, e4, e5, e6];
theta := [theta1, theta2, theta3, theta4, theta5, theta6];
omega := evalDG(add(theta[i] &wedge theta[7 - i], i = 1 .. 3));
g := evalDG(add(theta[i] &t theta[7 - i], i = 1 .. 3));
HodgeStar(g, theta1)

It is showing the following error,

Error, (in DifferentialGeometry:-Tensor:-HodgeStar) expected 1st argument to be a metric tensor. Received: _DG([["tensor", Alg1, [["cov_bas", "cov_bas"], []]], [`...`]])

How can I correct this? If not is there an alternative of doing what I am trying to do?

i try to get same result by substituation but i don't know what is mistake after i take second derivative is wronge i don't know how get same result as in paper did can anyone help  to calculate this part is not hard but is complicated ,How calculated second derivative and put in our ode to get the parameters?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

"          with(Student[ODEs][Solve]):"

_local(gamma)

declare(Omega(x, y, t)); declare(U(xi)); declare(u(x, y, t)); declare(Q(xi)); declare(V(xi)); declare(W(xi)); declare(f(xi))

Omega(x, y, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

u(x, y, t)*`will now be displayed as`*u

 

Q(xi)*`will now be displayed as`*Q

 

V(xi)*`will now be displayed as`*V

 

W(xi)*`will now be displayed as`*W

 

f(xi)*`will now be displayed as`*f

(2)

NULL

ode := -delta*(diff(diff(U(xi), xi), xi))+U(xi)*(w^2-gamma*U(xi)-beta-alpha) = 0

-delta*(diff(diff(U(xi), xi), xi))+U(xi)*(w^2-gamma*U(xi)-beta-alpha) = 0

(3)

ode1 := -delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

-delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

(4)

F := U(xi) = sum(tanh(xi)^(i-1)*(B[i]*sech(xi)+A[i]*tanh(xi)), i = 1 .. n)+A[0]

U(xi) = sum(tanh(xi)^(i-1)*(B[i]*sech(xi)+A[i]*tanh(xi)), i = 1 .. n)+A[0]

(5)

S := U(f(xi)) = sum(cos(f(xi))^(i-1)*(B[i]*sin(f(xi))+A[i]*cos(f(xi))), i = 1 .. n)+A[0]

U(f(xi)) = sum(cos(f(xi))^(i-1)*(B[i]*sin(f(xi))+A[i]*cos(f(xi))), i = 1 .. n)+A[0]

(6)

``

n := 2

2

(7)

eval(ode1, S)

-delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

(8)

Download complex-issue.mw

every thing is correct but i dont know why my PDE is not be zero, i did by another way is satidy but i change whole equation by sabstitutiin then i did ode test is satisfy by putting case in equation and solution with condition but when i want to use pdetest  test in pde is not satisfy ?

restart

_local(gamma)

with(PDEtools)

NULL

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(Omega(x, t)); declare(U(xi)); declare(V(xi)); declare(Theta(x, t))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

 

Theta(x, t)*`will now be displayed as`*Theta

(2)

xi := -t*tau+x

-t*tau+x

(3)

NULL

NULL

lambda := -tau/c; epsilon := -tau/c; delta := (2*c^2-gamma*tau)/(gamma-2*tau)

-tau/c

 

-tau/c

 

(2*c^2-gamma*tau)/(gamma-2*tau)

(4)

NULL

case1 := [c = RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)/gamma, A[0] = 0, A[1] = RootOf(_Z^2*gamma+2*tau), B[1] = 0]

[c = RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)/gamma, A[0] = 0, A[1] = RootOf(_Z^2*gamma+2*tau), B[1] = 0]

(5)

K := Omega(x, t) = RootOf(_Z^2*gamma+2*tau)*tanh(xi)*exp(I*gamma*(delta*t+x))

Omega(x, t) = -RootOf(_Z^2*gamma+2*tau)*tanh(t*tau-x)*exp(I*gamma*((2*c^2-gamma*tau)*t/(gamma-2*tau)+x))

(6)

NULL

pde1 := I*(diff(Omega(x, t), `$`(t, 2))-c^2*(diff(Omega(x, t), `$`(x, 2))))+diff(U(-t*tau+x)^2*Omega(x, t), t)-lambda*c*(diff(U(-t*tau+x)^2*Omega(x, t), x))+(1/2)*(diff(Omega(x, t), `$`(x, 2), t))-(1/2)*epsilon*c*(diff(Omega(x, t), `$`(x, 3))) = 0

I*(diff(diff(Omega(x, t), t), t)-c^2*(diff(diff(Omega(x, t), x), x)))-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0

(7)

NULL

subs(case1, pde1)

I*(diff(diff(Omega(x, t), t), t)-RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)^2*(diff(diff(Omega(x, t), x), x))/gamma^2)-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0

(8)

T := simplify(I*(diff(diff(Omega(x, t), t), t)-RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)^2*(diff(diff(Omega(x, t), x), x))/gamma^2)-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0)

(1/2)*(2*gamma^2*(tau*(diff(Omega(x, t), x))+diff(Omega(x, t), t))*U(-t*tau+x)^2+(diff(diff(diff(Omega(x, t), t), x), x))*gamma^2+tau*(diff(diff(diff(Omega(x, t), x), x), x))*gamma^2-(4*I)*((1/4)*gamma^3+tau-(1/2)*gamma)*tau*(diff(diff(Omega(x, t), x), x))+(2*I)*(diff(diff(Omega(x, t), t), t))*gamma^2)/gamma^2 = 0

(9)

pdetest(K, T)

-(1/2)*2^(1/2)*(-tau/gamma)^(1/2)*(-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau)))/(gamma^2*(gamma-2*tau)^2*(exp(2*t*tau)+exp(2*x))^3)

(10)

simplify(-(1/2)*2^(1/2)*(-tau/gamma)^(1/2)*((8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau)))/(gamma^2*(gamma-2*tau)^2*(exp(2*tau*t)+exp(2*x))^3))

-(-tau/gamma)^(1/2)*((I*gamma^3*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2-((1/8)*I)*tau*gamma^7+(((1/4)*I)*c^2+((1/2)*I)*tau^2-tau)*gamma^6+(4*tau^2+(-((3/2)*I)*c^2-(3/4)*I)*tau+2*c^2)*gamma^5+(-4*tau^3+((5/2)*I)*tau^2+(-8*c^2+2)*tau+I*(c^2+2)*c^2)*gamma^4-4*(((5/4)*I)*tau^2+(-2*c^2+3)*tau+I*c^2-(1/2)*I)*tau*gamma^3+6*(I*tau^2-2*I+4*tau)*tau^2*gamma^2+((24*I)*tau^3-16*tau^4)*gamma-(16*I)*tau^4)*exp((I*(t*tau-x)*gamma^2+2*((I*x-t)*tau-I*c^2*t-2*x)*gamma+4*t*tau^2+8*x*tau)/(-gamma+2*tau))+(-I*gamma^3*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2+((1/8)*I)*tau*gamma^7+(-((1/4)*I)*c^2-((1/2)*I)*tau^2-tau)*gamma^6+(4*tau^2+(((3/2)*I)*c^2+(3/4)*I)*tau+2*c^2)*gamma^5+(-4*tau^3-((5/2)*I)*tau^2+(-8*c^2+2)*tau-I*(c^2+2)*c^2)*gamma^4+4*(((5/4)*I)*tau^2+tau*(2*c^2-3)+I*c^2-(1/2)*I)*tau*gamma^3-6*(I*tau^2-2*I-4*tau)*tau^2*gamma^2+(-(24*I)*tau^3-16*tau^4)*gamma+(16*I)*tau^4)*exp((I*(t*tau-x)*gamma^2+2*((I*x-2*t)*tau-I*c^2*t-x)*gamma+8*t*tau^2+4*x*tau)/(-gamma+2*tau))+I*gamma^2*(exp((I*(t*tau-x)*gamma^2+2*(-I*c^2*t+I*x*tau-3*x)*gamma+12*x*tau)/(-gamma+2*tau))-exp((I*(t*tau-x)*gamma^2+2*((I*x-3*t)*tau-I*c^2*t)*gamma+12*t*tau^2)/(-gamma+2*tau)))*(gamma*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2-(1/8)*tau*gamma^5+((1/4)*c^2+(1/2)*tau^2)*gamma^4+tau*(-(3/2)*c^2+1/4)*gamma^3+(c^4-(3/2)*tau^2)*gamma^2+3*tau^3*gamma-2*tau^4))*2^(1/2)/(gamma^2*(exp(2*t*tau)+exp(2*x))^3*(-(1/2)*gamma+tau)^2)

(11)
 

 

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i want to factoring the (m+G'/G) in my long equation but i use some trick but still i can't get the exactly system and still G will remain in my system what should i factoring for remove this G(xi) from my system is all about factoring , my system of equation are wrong contain G(xi) How i can remove it by taking a factoring or any other technique,

not parameter is arbitrary except V and sigma''

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

u(x, y, z, t)*`will now be displayed as`*u

 

Q(xi)*`will now be displayed as`*Q

 

V(xi)*`will now be displayed as`*V

(2)

NULL

ode := (-V*a[2]+a[1])*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(-V*a[2]+a[1])*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(3)

F := sum(e[i]*(m+(diff(G(xi), xi))/G(xi))^i, i = -1 .. 1)

e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi))

(4)

D1 := diff(F, xi)

-e[-1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

(5)

NULL

S := diff(G(xi), `$`(xi, 2)) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

diff(diff(G(xi), xi), xi) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

(6)

E1 := subs(S, D1)

-e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

(7)

D2 := diff(E1, xi)

2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)

(8)

E2 := subs(S, D2)

2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)

(9)

D3 := diff(E2, xi)

-6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^4+4*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^3+2*e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*((2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/G(xi)+(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+3*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^2+6*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/G(xi)^2+6*(diff(G(xi), xi))^2*(diff(diff(G(xi), xi), xi))/G(xi)^3-6*(diff(G(xi), xi))^4/G(xi)^4)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/G(xi)+(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+3*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^2+6*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/G(xi)^2+6*(diff(G(xi), xi))^2*(diff(diff(G(xi), xi), xi))/G(xi)^3-6*(diff(G(xi), xi))^4/G(xi)^4)

(10)

E3 := subs(S, D3)

-6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^3/(m+(diff(G(xi), xi))/G(xi))^4+6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*((2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)+4*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+12*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/G(xi)^2-6*(diff(G(xi), xi))^4/G(xi)^4)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)+4*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+12*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/G(xi)^2-6*(diff(G(xi), xi))^4/G(xi)^4)

(11)

NULL

NULL

K := U(xi) = F

K1 := diff(U(xi), xi) = E1

K2 := diff(U(xi), `$`(xi, 2)) = E2

K3 := diff(U(xi), `$`(xi, 3)) = E3

NULL

L := eval(ode, {K, K1, K2, K3})

(-V*a[2]+a[1])*(2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3))+(e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi)))*(((-gamma+sigma)*k+b)*(e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi)))^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(12)

NULL

# rewritting rule

RR := isolate(m+diff(G(xi), xi)/(G(xi))=Phi, diff(G(xi), xi)/G(xi));

(diff(G(xi), xi))/G(xi) = Phi-m

(13)

# Apply RR and collect wrt Phi

subs(RR, L):
normal(%):
PhiN := collect(numer(lhs(%)), phi):
PhiD := denom(lhs(%%));

Phi^3*G(xi)^4

(14)



with(LargeExpressions):

LLE := collect(PhiN, Phi, Veil[phi] ):
LLE / PhiD = 0;

(Phi^6*phi[1]+3*Phi^5*phi[2]-Phi^4*phi[3]-Phi^3*phi[4]-Phi^2*phi[5]+Phi*phi[6]-phi[7])/(Phi^3*G(xi)^4) = 0

(15)

# phi[i] coefficients


phis := [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ]:

print~( phis ):

phi[1] = G(xi)^4*e[1]^3*((-gamma+sigma)*k+b)

 

phi[2] = e[1]^2*G(xi)^4*e[0]*((-gamma+sigma)*k+b)

 

phi[3] = -3*e[1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

 

phi[4] = (2*e[1]*(V*a[2]-a[1])*(diff(G(xi), xi))^3+3*e[1]*G(xi)*(2*m*mu+lambda)*(V*a[2]-a[1])*(diff(G(xi), xi))^2+e[1]*(V*a[2]-a[1])*G(xi)*((2*m*mu+lambda)^2*G(xi)+3*mu)*(diff(G(xi), xi))+G(xi)^2*(-(6*e[-1]*((-gamma+sigma)*k+b)*e[1]-a[1]*k^2+k*w*a[2]+((-gamma+sigma)*k+b)*e[0]^2-k*alpha-w)*e[0]*G(xi)+e[1]*mu*(2*m*mu+lambda)*(V*a[2]-a[1])))*G(xi)

 

phi[5] = -3*e[-1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

 

phi[6] = 4*((1/2)*(V*a[2]-a[1])*(diff(G(xi), xi))^3+(3/2)*(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(3/4)*mu)*G(xi)*(diff(G(xi), xi))+(1/2)*((3/2)*e[0]*((-gamma+sigma)*k+b)*e[-1]*G(xi)+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu)*G(xi)^2)*e[-1]*G(xi)

 

phi[7] = 8*e[-1]*((1/4)*(V*a[2]-a[1])*(diff(G(xi), xi))^4+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^3+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(1/2)*mu)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu*G(xi)^2*(diff(G(xi), xi))+(1/4)*(-(1/2)*((-gamma+sigma)*k+b)*e[-1]^2*G(xi)^2+mu^2*(V*a[2]-a[1]))*G(xi)^2)

(16)

# WATCHOUT: you have 9 coefficients and so its desirable to have the same number of unknowns

unknowns := indets(rhs~(phis), {e[-1],e[0],e[1],'identical'(mu),'identical'(lambda),'identical'(a[1]),'identical'(alpha)});

COEFFS := solve(rhs~(phis), unknowns)

{alpha, lambda, mu, a[1], e[-1], e[0], e[1]}

 

{alpha = alpha, lambda = lambda, mu = mu, a[1] = a[1], e[-1] = 0, e[0] = 0, e[1] = 0}, {alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}, {alpha = (1/2)*(-G(xi)^4*gamma*k^3*e[-1]^2+G(xi)^4*k^3*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*k^2*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*k^2*m*mu*a[2]+G(xi)^4*b*k^2*e[-1]^2+4*G(xi)^2*(diff(G(xi), xi))*k*m*mu^2*w*a[2]-4*G(xi)*(diff(G(xi), xi))^3*k*m*mu*w*a[2]-2*G(xi)^2*V*k^2*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*k^2*mu*a[2]-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*mu*a[2]+2*(diff(G(xi), xi))^4*V*k^2*a[2]+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*a[2]-4*G(xi)^2*(diff(G(xi), xi))*m*mu^2*w+2*G(xi)^2*k*mu^2*w*a[2]+4*G(xi)*(diff(G(xi), xi))^3*m*mu*w-2*G(xi)*(diff(G(xi), xi))^2*k*mu*w*a[2]+2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*mu*w*a[2]-2*(diff(G(xi), xi))^4*k*w*a[2]-2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*w*a[2]-2*G(xi)^2*mu^2*w+2*G(xi)*(diff(G(xi), xi))^2*mu*w-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*mu*w+2*(diff(G(xi), xi))^4*w+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*w)/((2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4)*k), lambda = RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)/G(xi), mu = mu, a[1] = -(1/2)*(-G(xi)^4*gamma*k*e[-1]^2+G(xi)^4*k*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*m*mu*a[2]+G(xi)^4*b*e[-1]^2-2*G(xi)^2*V*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*mu*a[2]-2*mu*G(xi)*(diff(G(xi), xi))*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2]+2*(diff(G(xi), xi))^4*V*a[2]+2*(diff(G(xi), xi))^3*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2])/(2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4), e[-1] = e[-1], e[0] = 0, e[1] = 0}

(17)

case1 := COEFFS[2]

{alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}

(18)

NULL

F1 := subs(case1, F)

e[0]

(19)

F2 := subs(case1, ode)

(-a[2]*V-(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2)*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2+k*e[0]^2*gamma-k*e[0]^2*sigma-b*e[0]^2-k*w*a[2]+k*alpha+(w*a[2]-alpha)*k) = 0

(20)

W := U(xi) = F1

U(xi) = e[0]

(21)

NULL

E := diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

(22)

W1 := subs(E, W)

U(xi) = e[0]

(23)

W2 := subs(case1, W1)

U(xi) = e[0]

(24)

W3 := rhs(U(xi) = e[0])

e[0]

(25)

W4 := convert(W3, trig)

e[0]

(26)

W5 := W4

e[0]

(27)

odetest(W2, F2)

0

(28)

Download G-factoring.mw

I’m trying to solve a stiff system 1-D PDEs numerically in Maple but I’m getting the following error:

“Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence”

I included a picture of the PDEs and their BCs in the attached maple file. For easy reading, the attached file includes highlighted sections for parameters and variables. You can skip those to PDEs, BCs and ICs sections at the end of the document to reach the error I’m facing.

For reference, I used another software to solve the system and I was able to get the results in few seconds, so I think it is solvable. However, personally I prefer to use Maple so any inputs, insights, workarounds that I could use to handle the system in Maple would be of great help to me. Thank you.

question.mw

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