Re: Solving Weissinger's ODE
- To: mathgroup at smc.vnet.net
- Subject: [mg104870] Re: Solving Weissinger's ODE
- From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
- Date: Thu, 12 Nov 2009 06:03:47 -0500 (EST)
- References: <hde08e$spq$1@smc.vnet.net>
Hi Virgil,
I don't think the solution you provide is right. It doesn't fulfill
the initial condition and you won't get zero if you fill it in in the
equation. If you plot both Mathematica's solution and the one you name
you can see it's a close but not perfect match
Cheers -- Sjoerd
On Nov 11, 11:30 am, Virgil Stokes <v... at it.uu.se> wrote:
> I can not see why the following does not work as expected,
>
> s = NDSolve[{t * (y[t])^2 * (y'[t])^3 - (y[t])^3 * (y'[t])^2 + t *
> (t^2 + 1) * y'[t] - t^2 *y[t] == 0, y[1] == Sqrt[3/2]}, y[t], {t, 1, 10}]
>
> Note, the solution to this nonlinear, non-autonomous, implicit ODE for
> initial condition y[1] = Sqrt[3/2] is just y[t] = Sqrt[t^2 + 1].
>
> Any suggestions on how to obtain the solution (either analytic or
> numerical) would be appreciated.
>
> --V. Stokes