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Re: Solving Weissinger's ODE
*To*: mathgroup at smc.vnet.net
*Subject*: [mg104867] Re: Solving Weissinger's ODE
*From*: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
*Date*: Thu, 12 Nov 2009 06:03:12 -0500 (EST)
*References*: <hde08e$spq$1@smc.vnet.net>
First of all Sqrt[t^2+1] does not satisfy your IC.
Second, you get three solutions to the DE from NDSolve due to the
nonlinear terms. The three solutions satisfy the DE and the IC. Two of
the solutions are complex and are conjugates of each other. Seems ok to me.
Kevin
Virgil Stokes 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
>
>
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