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Re: Solving Weissinger's ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg104892] Re: Solving Weissinger's ODE
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Thu, 12 Nov 2009 06:08:08 -0500 (EST)
• References: <hde08e$spq$1@smc.vnet.net>

"Virgil Stokes" <vs at it.uu.se> wrote in message 
news:hde08e$spq$1 at smc.vnet.net...
>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
>
>

Hello;

Actually the numerical solution given by NDSolve is very good !

maxTime = 30;

eq = t*y[t]^2*Derivative[1][y][t]^3 - y[t]^3*Derivative[1][y][t]^2 +t*(t^2 + 
1)*Derivative[1][y][t] - t^2*y[t];

sol = NDSolve[{eq == 0, y[1] == Sqrt[3/2]}, y[t], {t, 1, maxTime}];

data = Table[{t, Evaluate[y[t] /. sol[[1,1]]]}, {t, 1, 30}];

trueSolution = Sqrt[t^2 + 0.5];

p1 = Plot[trueSolution, {t, 1, maxTime}, PlotRange -> All, AxesOrigin -> {0, 
0}, PlotStyle -> Red];

p2 = ListPlot[data, PlotMarkers -> {Graphics[Disk[]], 0.02},AxesOrigin -> 
{0, 0}];

Show[p1, p2, PlotLabel -> "true vs numerical solution for weissinger ODE"]

--Nasser