Trying to obtain an explicit solution of a second order ODE
Subject: Trying to obtain an explicit solution of a second order ODE
From: Rupert Swarbrick
Date: Wed, 17 Apr 2013 14:27:27 +0100
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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