Varying a constant in an ODE to Manipulate solution

• To: mathgroup at smc.vnet.net
• Subject: [mg126853] Varying a constant in an ODE to Manipulate solution
• From: Narasimham <mathma18 at hotmail.com>
• Date: Wed, 13 Jun 2012 04:57:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Same topic is continued. Thanks to Murray Eisenberg and Bob Hanlon

All variables or a single variable are easily pocked out from sol[c_]
list for plotting.
But how to pick out two out of them for ParametricPlot  ( 2D) ?

sol[c_] := {x[t], y[t], z[t]} /.
First[NDSolve[{y''[t] + Sin[y[t]/c] == 0, y'[0] == 0,
y[0] == 1/(1 + c), x'[t] == t, x[0] == c^2,
z'[t] == 2 c x[t] - y[t], z[0] == 2}, {x, y, z}, {t, -3, 3}]]
Manipulate[
Plot[Evaluate[sol[c]], {t, -3, 3}, PlotStyle -> {Red, Thick},
AspectRatio -> Automatic,
PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}]
Manipulate[
Plot[Evaluate[sol[c][[1]]], {t, -3, 3}, PlotStyle -> {Red, Thick},
AspectRatio -> Automatic,
PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}]
" 2 parameter Dynamic manipulation not OK "
Manipulate[
Plot[{Evaluate[sol[c][[1]]], Evaluate[sol[c][[1]]]}, {t, -3, 3},
PlotStyle -> {Green, Thick}, AspectRatio -> Automatic,
PlotRange -> {{-3, 3}, {-10, 10}}], {c, -0.5, 2, 0.2}]

Regards
Narasimham

```

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