On 12 bře, 21:19, Guillaume <[email protected]> wrote:
> > No, AFAIK, nothing other than explicit substitution with .subs().
>
> Hello,
>
> there are a few weird results. I'd like to solve this homogenous edo :
>
> $tx'=x+\sqrt{x^2+y^2}$.
>
> using x=tu
>
> sage: t=var('t')
> sage: x(t) = function('x',t)
> sage: id(t)=t
> sage: u=function('u',t)
> sage: d=diff(u*id,t)
>
Is this what you want?
sage: t=var('t')
sage: x= function('x',t)
sage: id(t)=t
sage: u=function('u',t)
sage: d=diff(u*id,t)
sage: assume(t>0)
sage: DE=(t*d==x+sqrt(t**2+x**2)).subs_expr(x==u*id)
sage: A=desolve(DE,u)
sage: C=var('C')
sage: A._maxima_().ev(logarc=true).sage().solve(u)[0].subs(c=log(C))
u(t) == C*t - sqrt(u(t)^2 + 1)
sage: eq = u == C*t - sqrt(u^2 + 1)
sage: ((eq-C*t)^2).solve(u)
[u(t) == 1/2*(C^2*t^2 - 1)/(C*t)]
The fact that the integral in A in not evaluated is probably a bug.
You may want to open trac on this and test, if this bug is inside
Maxima or in Sage interface to Maxima.
Robert
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