Maple 2024 Questions and Posts

Can anyone determine my mistake my odetest not wor...

Asked by: salim-barzani 1555

February 08 2025

0 2

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

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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))

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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

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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]]

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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)))

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Download ode.mw

why when i take integral from equation exponential...

Asked by: salim-barzani 1555

February 08 2025

0 4

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

g1.mw

String and parse on decimal number...

Asked by: nm 11353

February 08 2025

1 1

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.

Download string_of_decimal_number.mw

How to get solution Soll11 for the reduced Liouvil...

Asked by: janhardo 685

February 02 2025

0 5

The modified Liouville equation

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How to solve this pde for a general solution ?

The general solution in this form exist.

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restart;

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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) = 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

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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 ?

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>	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? :

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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) = 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

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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));

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

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, ,

Question : how do i arrive on Soll11 in Maple ?

Download liouville_reduced_2-2-2025_mprimes_vraag.mw

How find true parameter which satisfy pde?...

Asked by: salim-barzani 1555

January 28 2025

0 2

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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

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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)

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

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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)

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-(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

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

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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

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

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

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

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

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

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

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

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

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Download hard_parameters.mw

How can fix `[Length of output exceeds limit of 10...

Asked by: salim-barzani 1555

January 26 2025

1 4

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

Customized Key Bindings?...

Asked by: studentX369 30

January 25 2025

2 6

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.

Why my out come is different by same method and sa...

Asked by: salim-barzani 1555

January 25 2025

0 0

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

How to use HodgeStar command for forms on Lie Alge...

Asked by: GeometerFromHell 0

January 20 2025

0 0

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?

How do complicated substitution in ode?...

Asked by: salim-barzani 1555

January 17 2025

1 0

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?

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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]

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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]

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Download complex-issue.mw

why my pdetest not satisfy?...

Asked by: salim-barzani 1555

January 10 2025

0 10

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 ?

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NULL

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

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

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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]

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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))

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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)

>

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)

>

(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)

>

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>

(11)

Download pdetest.mw

How make a system of equation by using special fa...

Asked by: salim-barzani 1555

January 06 2025

0 4

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''

>

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>

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.

>

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>

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>

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)

>

-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)

>

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>

-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)

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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(%%));

(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[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)

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>	# 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 = 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]

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

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(-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

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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)

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Download G-factoring.mw

system of 1-D PDEs numerically...

Asked by: mayzal 25

January 05 2025

1 8

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

Bug report: Error, (in dsolve) invalid subscript s...

Asked by: nm 11353

December 27 2024

0 2

I do not remember if I reported this before or not. Can't find it. Just in case, I am posting this.

If someone find it is duplicate, feel free to delete this. But this is in latest Maple 2024.2. May be this can be fixed in time by Maple 2025 version.

>

restart;

>	interface(version);

>	Physics:-Version();

>

libname;

$"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"$

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0;

(diff(y(x), x))/y(x)-(3/2)*(4*x^2+y(x)^2+1)/(x*(4*x^2+y(x)^2-2-2*x)) = 0

>	DEtools:-odeadvisor(ode);

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

>

restart;

>	infolevel[dsolve]:=5;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

trying inverse linear

trying homogeneous types:

trying Chini

differential order: 1; looking for linear symmetries

trying exact

Looking for potential symmetries

trying inverse_Riccati

trying an equivalence to an Abel ODE

equivalence obtained to this Abel ODE: diff(y(x),x) = 3/2*(4*x^2+1)/x/(2*x^2-x-1)*y(x)-(x^2+2*x+3)/x/(2*x^2-x-1)^2*y(x)^2+3/8*(2*x+3)/(2*x^2-x-1)^3/x*y(x)^3

trying to solve the Abel ODE ...

The relative invariant s3 is: -1/432*(8*x^4+40*x^3+45*x^2-270*x+135)/x^3/(x-1)^6/(2*x+1)^4

The first absolute invariant s5^3/s3^5 is: 729/16*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^3/(2*x+1)^4/(8*x^4+40*x^3+45*x^2-270*x+135)^5

The second absolute invariant s3*s7/s5^2 is: 1/3*(8*x^4+40*x^3+45*x^2-270*x+135)*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^2

...checking Abel class AIL (45)

...checking Abel class AIL (310)

...checking Abel class AIR (36)

...checking Abel class AIL (301)

...checking Abel class AIL (1000)

...checking Abel class AIL (42)

...checking Abel class AIL (185)

...checking Abel class AIA (by Halphen)

...checking Abel class AIL (205)

...checking Abel class AIA (147)

...checking Abel class AIL (581)

...checking Abel class AIL (200)

...checking Abel class AIL (257)

...checking Abel class AIL (400)

...checking Abel class AIA (515)

...checking Abel class AIR (1001)

...checking Abel class AIA (201)

...checking Abel class AIA (815)

Looking for potential symmetries

... changing x -> 1/x, trying again

Looking for potential symmetries

The third absolute invariant s5*s7/s3^4 is: 243/16*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(2*x+1)^4*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)/(8*x^4+40*x^3+45*x^2-270*x+135)^4

-> ======================================

-> ...checking Abel class D (by Appell)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {4/27} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class B (by Liouville)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {1, 4, 1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class A (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class C (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {2, -11676447873119/75975070592769, 9/5, 15632211369872/75439744512117, 46273613050865/52325357771027, 75312059745574/25138886548531} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 9/5 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.6

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-4, 16} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.8

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -116457391291688/45108305127449, -96869842492381/35485755507516, -36964550865207/94238117721032, -32286830321303/11596568583712, 32286830321303/11596568583712, 36964550865207/94238117721032, 96869842492381/35485755507516, 116457391291688/45108305127449} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.9

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-2/9, -1/9} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.51

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -94917840318055/84247876515289, -85939756880989/51399391393709, -82210125508529/36853933366676, -74381886667083/82545981233858, -41168492684238/33804146399567, -15658703496425/19275443365317, -9175348901453/101481647952193, 3/4, 15/4, 5568553686203/113599855351490, 12774469621703/63437040534358, 17836021821409/102823494563886, 39657708622139/74009717243016, 82495450887526/27663991325651, 86656182727564/45157560524183, 90074893410229/54954593917906, 100200889070747/32282555481919, 113612565327585/103754255779069} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 15/4 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.5

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-1, 1, -113553630998996/78694251194667, -112790344818825/35834119404842, -104905620984375/18860524785743, -95409943222181/78810323073434, -77648002983645/31218435062578, -67259194033608/9576982470445, -46892223838816/86694928762723, -45901561561111/29768419326991, -34674701564566/6522678435631, 26154715634141/21099761863911, 42841215778132/81925179545457, 52638927823233/15127919203723, 54069389554571/5444364811188, 54445812264368/10328928623117, 56815569067370/40738034746481, 75614540760757/62881656939350, 76459718737483/64786816765621, 85896394925571/88677987470966, 90623073438172/24246571690325, 103628692054633/17857341616628, 117754725919014/60191028908095} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -1 leads to a useless solution (F does not depend on x)

_____________________________

C = -113553630998996/78694251194667 leads to a useless solution (F does not depend on x)

_____________________________

C = -112790344818825/35834119404842 leads to a useless solution (F does not depend on x)

_____________________________

C = -104905620984375/18860524785743 leads to a useless solution (F does not depend on x)

_____________________________

C = -95409943222181/78810323073434 leads to a useless solution (F does not depend on x)

_____________________________

C = -77648002983645/31218435062578 leads to a useless solution (F does not depend on x)

_____________________________

C = -67259194033608/9576982470445 leads to a useless solution (F does not depend on x)

_____________________________

C = -46892223838816/86694928762723 leads to a useless solution (F does not depend on x)

_____________________________

C = -45901561561111/29768419326991 leads to a useless solution (F does not depend on x)

_____________________________

C = -34674701564566/6522678435631 leads to a useless solution (F does not depend on x)

_____________________________

C = 26154715634141/21099761863911 leads to a useless solution (F does not depend on x)

_____________________________

C = 42841215778132/81925179545457 leads to a useless solution (F does not depend on x)

_____________________________

C = 52638927823233/15127919203723 leads to a useless solution (F does not depend on x)

_____________________________

C = 54069389554571/5444364811188 leads to a useless solution (F does not depend on x)

_____________________________

C = 54445812264368/10328928623117 leads to a useless solution (F does not depend on x)

_____________________________

C = 56815569067370/40738034746481 leads to a useless solution (F does not depend on x)

_____________________________

C = 75614540760757/62881656939350 leads to a useless solution (F does not depend on x)

_____________________________

C = 76459718737483/64786816765621 leads to a useless solution (F does not depend on x)

_____________________________

C = 85896394925571/88677987470966 leads to a useless solution (F does not depend on x)

_____________________________

C = 90623073438172/24246571690325 leads to a useless solution (F does not depend on x)

_____________________________

C = 103628692054633/17857341616628 leads to a useless solution (F does not depend on x)

_____________________________

C = 117754725919014/60191028908095 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.52

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-5, -4, -3, 0, 1, 2, -3/2} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.53

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-3, -1, 1, 2, -3/2, -2/3, -1/2} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -3 leads to a useless solution (F does not depend on x)

_____________________________

C = -3/2 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

trying to map the Abel into a solvable 2nd order ODE

...checking Abel class AIA 2-parameter, reducible to Riccati

Error, (in dsolve) invalid subscript selector

>

restart;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

>	tracelast;

Error, (in dsolve) invalid subscript selector

Download dsolve_invalid_subscript_dec_27_2024.mw

why taking double derivative with two different in...

Asked by: salim-barzani 1555

December 27 2024

0 6

I did a lot of time but this time i don't know why not run any one have idea?

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