Trying to obtain an explicit solution of a second order ODE
Subject: Trying to obtain an explicit solution of a second order ODE
From: Stavros Macrakis
Date: Wed, 17 Apr 2013 09:41:24 -0400
Dear Maxima mailing list colleagues,
May I suggest you read your email most-recent-first so that instead of
duplicating solutions to user questions or providing solutions which are
less good than those already published, you improve on (or critique...)
previous solutions?
-s
On Wed, Apr 17, 2013 at 9:27 AM, Rupert Swarbrick <rswarbrick at gmail.com>wrote:
> Jaime Villate <villate at fe.up.pt> writes:
> > Hi,
> > I don't think he needs to use ic2, and the solution given by
> > solve(%,y) has failed to give y as a function of x.
> > You can try giving Maxima a little help:
> >
> > (%i2) de: 'diff(y,x,2)=-C*'diff(y,x)^2/y$
> >
> > (%i3) sol: ode2(de,y,x);
> >
> > (%o3) y*%e^(log(y)*C)/(%k1*C+%k1) = x+%k2
> >
> > (%i4) ratsubst(y^C, %e^(log(y)*C), sol);
> >
> > (%o4) y^(C+1)/(%k1*C+%k1) = x+%k2
> >
> > which would mean that the general solution is of the form: A y^(C+1)
> > = x + B
> > where A and B are two constants.
>
> Oops, good point. I hadn't noticed that y appeared twice. Thanks!
>
> Rupert
>
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