Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Which version of Maple contains its most optimal and elegant coding, regardless of utility,  and was it the product of someone's direct creative input (not auto-coded with AI for example).

As an aside, there's a spelling mistake in the word "separate" below within the "Tags" instruction:

"Tags are words are used to describe and categorize your content. Combine multiple words with dashes(-), and seperate tags with spaces."

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

restart;
Fig:=proc(t)
local a,b,c,A,B,C,Oo,P,NorA,NorB,NorC,lieu,Lieu,dr,tx:
uses plots, geometry;
a := 11:b := 7:
c := sqrt(a^2 - b^2):

point(A, a*cos(t), b*sin(t)):
point(B, a*cos(t + 2/3*Pi), b*sin(t + 2/3*Pi)):
point(C, a*cos(t + 4/3*Pi), b*sin(t + 4/3*Pi)):
point(Oo,0,0):
lieu:=a^2*x^2+b^2*y^2-c^4/4=0:
Lieu := implicitplot(lieu, x = -a .. a, y = -b .. b, color = green):

line(NorA, y-coordinates(A)[2] =((a^2*coordinates(A)[2])/(b^2*coordinates(A)[1]))*(x-coordinates(A)[1]),[x, y]):
line(NorB, y-coordinates(B)[2] =((a^2*coordinates(B)[2])/(b^2*coordinates(B)[1]))*(x-coordinates(B)[1]), [x, y]):
line(NorC, y-coordinates(C)[2] =((a^2*coordinates(C)[2])/(b^2*coordinates(C)[1]))*(x-coordinates(C)[1]),[x, y]):
intersection(P,NorA,NorB):

ellipse(p, x^2/a^2 + y^2/b^2 - 1, [x, y]);

tx := textplot([[coordinates(A1)[], "A"],[coordinates(A2)[], "B"], [coordinates(C)[], "C"], [coordinates(Oo)[], "O"],#[coordinates(P)[], "P"]], font = [times, bold, 16], align = [above, left]):
dr := draw([p(color = blue),NorA(color=red,NorB(color=red),NorC(color=red),p(color=blue),
Oo(color = black, symbol = solidcircle, symbolsize = 8), P(color = black, symbol = solidcircle, symbolsize = 8)]):
display(dr,tx,Lieu,scaling=constrained, axes=none,title = "Les triangles inscrits dans une ellipse ont leur centre de gravité en son centre . Lieu du point de concours des perpendicalaires issues des sommets", titlefont = [HELVETICA, 14]);
end:

Error, `:=` unexpected
plots:-animate(Fig, [t], t=0.1..2*Pi, frames=150);
 

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

I'd like to know the details of the method Statistics:-Mean uses to numerically estimate the expectation of a random variable.

showstat seems of no use and neither seems to be LibraryTools[Browse]();

Here are two examples: the first one (1D) suggests  Statistics:-Mean could use some evalf/Int method, but the conclusion to draw from the second example (R2 --> R) is less clear.

How_does_Mean_proceed.mw

Thanks in advance

PS: I already asked a similar question months ago but didn't get any reply.
       Even answers such as “We don't know” or “We don't care” would suit me better than their absence.

scmch.mw

I can't get a graph. Is this code is correct.Please help.

How to integrate eq (4)? Since 'a', 'b', and 'c' are constant. 

restart

with(DEtools)

declare(z(x), y(x))

declare(z(x), y(x))

(1)

eq1 := (1/2)*(-z(x)^3-2*c*z(x))*(diff(diff(y(x), x), x))-((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x)) = 0

(1/2)*(-z(x)^3-2*c*z(x))*(diff(diff(y(x), x), x))-((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x)) = 0

(2)

eq2 := simplify(z(x)*eq1)

-z(x)*(z(x)*((1/2)*z(x)^2+c)*(diff(diff(y(x), x), x))+((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x))) = 0

(3)

eq3 := eval(int(lhs(eq2), x))

int(-z(x)*(z(x)*((1/2)*z(x)^2+c)*(diff(diff(y(x), x), x))+((z(x)^2+2*c)*(diff(y(x), x))+b*z(x)^2+c*k+a)*(diff(z(x), x))), x)

(4)

NULL

Download integration.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

Hi All,

Maple is changing fast. It is not possible to run some older codes. 

Is it possible those who have a valid Maple license to have the old versions free of charge?

I have Maple 7, 2018, 2021 licenses but still have problem running older codes.

restart; with(PDEtools); declare(F(x, t), G(x, t), H(x, t))

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

 

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

 

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

(1)

q := 1-(diff(diff(log(F(x, t)), x), t)); r := G/F; s := H/F

1-(diff(diff(F(x, t), t), x))/F(x, t)+(diff(F(x, t), x))*(diff(F(x, t), t))/F(x, t)^2

 

G/F

 

H/F

(2)

r1s1 := r*s; r1s1der := diff(r1s1(x, t), x)

qt := diff(q(x, t), t)

eq1B := F(x, t)^3*(qt+r1s1der) = 0; eq12B := simplify(expand(eq1B))

-F(x, t)^3*(diff((diff(diff(F(x, t), t), x))(x, t), t))/(F(x, t))(x, t)+F(x, t)^3*(diff(diff(F(x, t), t), x))(x, t)*(diff((F(x, t))(x, t), t))/(F(x, t))(x, t)^2+F(x, t)^3*(diff((diff(F(x, t), x))(x, t), t))*(diff(F(x, t), t))(x, t)/(F(x, t))(x, t)^2-2*F(x, t)^3*(diff(F(x, t), x))(x, t)*(diff(F(x, t), t))(x, t)*(diff((F(x, t))(x, t), t))/(F(x, t))(x, t)^3+F(x, t)^3*(diff(F(x, t), x))(x, t)*(diff((diff(F(x, t), t))(x, t), t))/(F(x, t))(x, t)^2+F(x, t)*(diff(G(x, t), x))*H(x, t)-2*G(x, t)*H(x, t)*(diff(F(x, t), x))+F(x, t)*G(x, t)*(diff(H(x, t), x)) = 0

(3)

D_x_x_G_F := (diff(G(x, t), x, x))*F(x, t)-2*(diff(G(x, t), x))*(diff(F(x, t), x))+G(x, t)*(diff(F(x, t), x, x)); D_t_t_F_F := F(x, t)*(diff(F(x, t), `$`(t, 2)))-2*(diff(F(x, t), t))^2

(diff(diff(G(x, t), x), x))*F(x, t)-2*(diff(G(x, t), x))*(diff(F(x, t), x))+G(x, t)*(diff(diff(F(x, t), x), x))

 

F(x, t)*(diff(diff(F(x, t), t), t))-2*(diff(F(x, t), t))^2

(4)

NULL

rxt := diff(diff(r(x, t), x), t)

eq2B := -2*q*r+rxt = 0

eq22B := simplify(expand(eq2B))

((-F*F(x, t)*G(x, t)+2*G*F(x, t)^2)*(diff(diff(F(x, t), t), x))+(diff(diff(G(x, t), t), x))*F*F(x, t)^2+((2*F*G(x, t)-2*G*F(x, t))*(diff(F(x, t), x))-F*(diff(G(x, t), x))*F(x, t))*(diff(F(x, t), t))-(diff(G(x, t), t))*(diff(F(x, t), x))*F*F(x, t)-2*G*F(x, t)^3)/(F*F(x, t)^3) = 0

(5)

sxt := diff(diff(s(x, t), x), t)

eq3B := -2*q*s+sxt = 0

eq32B := simplify(expand(eq3B))

((-F*F(x, t)*H(x, t)+2*H*F(x, t)^2)*(diff(diff(F(x, t), t), x))+(diff(diff(H(x, t), t), x))*F*F(x, t)^2+((2*F*H(x, t)-2*H*F(x, t))*(diff(F(x, t), x))-F*(diff(H(x, t), x))*F(x, t))*(diff(F(x, t), t))-(diff(H(x, t), t))*(diff(F(x, t), x))*F*F(x, t)-2*H*F(x, t)^3)/(F*F(x, t)^3) = 0

(6)

"#`# How to simplify Eqs. (3), (5) and (6) and write in terms of following bilineat operators` by using (4)"?""

NULL

NULL

Download BE.mw

Hi,

Experiencing the following problem.  One of our servers was cloned, the GUID was replaced and then rejoined to the domain.  All applications are working exept Maple.  The application launches but then closes right away.  No error messages provided so not sure where else to look for possible fixes to this problem.  The application is runing on Server 2022.

Thank you.

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

5 6 7 8 9 10 11 Last Page 7 of 2215