Try x^(1+a)/(1+a) --> w
%i49) eq : x + 1/(3*x^3*(y+x)^3)+w = %c;
(%o49) 1/(3*x^3*(y+x)^3)+x+w=%c
(%i50) sol : solve(eq,y)$
(%i51) reveal(sol,3);
(%o51) [y=Sum(2),y=Sum(2),y=Quotient]
(%i54) ratsimp(sol);
(%o54)
[y=-(2*3^(1/3)*x^2*(x+w-%c)^(1/3)-sqrt(3)*%i-1)/(2*3^(1/3)*x*(x+w-%c)^(1/3)),y=-(2*3^(1/3)*x^2*(x+w-%c)^(1/3)+sqrt(3)*%i-1)/(2*3^(1/3)*x*(x+w-%c)^(1/3)),y=-(3*x^2*(x+w-%c)^(1/3)+9^(1/3))/(3*x*(x+w-%c)^(1/3))](%i49)
eq : x + 1/(3*x^3*(y+x)^3)+w = %c;
(%o49) 1/(3*x^3*(y+x)^3)+x+w=%c
(%i50) sol : solve(eq,y)$
(%i51) reveal(sol,3);
(%o51) [y=Sum(2),y=Sum(2),y=Quotient]
(%i54) ratsimp(sol);
(%o54)
[y=-(2*3^(1/3)*x^2*(x+w-%c)^(1/3)-sqrt(3)*%i-1)/(2*3^(1/3)*x*(x+w-%c)^(1/3)),y=-(2*3^(1/3)*x^2*(x+w-%c)^(1/3)+sqrt(3)*%i-1)/(2*3^(1/3)*x*(x+w-%c)^(1/3)),y=-(3*x^2*(x+w-%c)^(1/3)+9^(1/3))/(3*x*(x+w-%c)^(1/3))]
Without x^(1+a)/(1+a) --> w, Maxima struggles with simplification, I
think.
A little carbon-based computing wins. Of course, maxima should be able to
do this without help.
Barton
maxima-bounces at math.utexas.edu wrote on 01/27/2010 12:21:03 PM:
> [image removed]
>
> Re: [Maxima] max time limit for solve
>
> nijso beishuizen
>
> to:
>
> maxima
>
> 01/27/2010 12:20 PM
>
> Sent by:
>
> maxima-bounces at math.utexas.edu
>
> Hi,
>
> The equation I try to solve is the final step in the solution of a
> nonlinear ode. The solution in the paper
> (of Cheb-Terrab and Kolokolnikov, it's on ArXiv) is given in implicit
form as:
>
> sol : x + 1/(3*x^3*(y+x)^3)+x^(1+a)/(1+a) = %c;
>
> In the algorithm I manage to get the left hand side of sol [well,
> actually I get factor(ratsimp(sol))]. I do not know beforehand that
> the solution should remain in implicit form, although you can
> rewrite the solution as y(x)=(..) . I then do
>
> solve(sol,y);
>
> After a couple of minutes it starts returning an answer and it takes
> 10 minutes to output the answer.
> Yesterday I tried it with emacs+maxima and I never got any answer
> returned, this is with xmaxima.
>
> Actually, maple finds the 3 compact explicit solutions of the above
> equation, and when you solve the original ode, it knows that the
> implicit form is somehow more appropriate to return (it returns sol
> instead of the result of solve(sol,y)).
> Instead of killing solve after x minutes, is there a way to improve
> the result of solve, or a way of determining beforehand that going
> for an explicit solution of sol might be a bad idea?
>
> Regards,
> Nijso
>
>
>
>
>
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