Re: NDolve + ParametricPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg67533] Re: [mg67513] NDolve + ParametricPlot
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 30 Jun 2006 04:13:57 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```sol = NDSolve[{x''[t] == x[t], x[0] == 1, x'[0] == 1.1},
x, {t, 0, 3}];
Plot[x[t] /. sol, {t, 0, 3}];
Plot[D[x[t]] /. sol, {t, 0, 3}];
ParametricPlot[{x[t] , D[x[t]]}/.sol, {t, 0, 3}];

The exact solution is

x[t]/.DSolve[{x''[t] == x[t], x[0] == 1, x'[0] == 11/10},
x[t], t][[1]]

((1/20)*(-1 + 21*E^(2*t)))/E^t

%//FullSimplify

Cosh[t] + (11*Sinh[t])/10

Bob Hanlon

---- Paolo Pani <paolopani at RIMUOVEREgmail.com> wrote:
> Hi, i'm new with Mathematica..i'm getting mad with expressions like this:
>
> sol = NDSolve[{x''[t] == x[t], x[0] == 1, x'[0] == 1.1}, x, {t, 0, 3}];
> Plot[x[t] /. sol, {t, 0, 3}];
> Plot[D[x[t]] /. sol, {t, 0, 3}];
> ParametricPlot[Evaluate[{x[t] /. sol, D[x[t] /. sol]}], {t, 0, 3}];
>
> The first two Plots are ok, the third give me:
>
>
>
> ParametricPlot::pptr: {InterpolatingFunction[{{0., 3.}}, {2, 2, True,
> Real, \
> {3}, {0}}, {{\[LeftSkeleton]1\[RightSkeleton]}}, {{0, 3, 6, 9, 12, 15, 18, \
> 21, 24, 27, \[LeftSkeleton]32\[RightSkeleton]}, {1., 1.1, \[LeftSkeleton]8\
> \[RightSkeleton], \[LeftSkeleton]113\[RightSkeleton]}}, {Automatic}][t]}
> does \
> not evaluate to a pair of real numbers at t = 1.25`*^-7.
>
>
>
>
> ... and "More..." does tell nothing more.
>
> Where is my mistake?
>
> Thanks and sorry for my bad english
>
> Paolo
>

```

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