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Re: Problem in solving Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg120043] Re: Problem in solving Differential Equation
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Wed, 6 Mar 2013 05:55:52 -0500 (EST)
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• References: <20130306031441.3FE5E665F@smc.vnet.net>

Arguments to functions (e.g., Sin, Cos) must be enclosed in squares
brackets: Sin[x[t]] and Cos[x[t]]

Clear[x];
\[Omega] = -2;
eqn =
  x''[t] + Sin[x[t]] - \[Omega]^2 Sin [x[t]] Cos[x[t]] == 0 //
   Simplify;
sol = NDSolve[
    {eqn, x[0] == 1/2, x'[0] == 0},
    x[t], {t, 0, 25}][[1]];
ParametricPlot[
 Evaluate[{x[t] /. sol, D[x[t] /. sol, t]}],
 {t, 0, 25},
 Frame -> True,
 Axes -> False,
 FrameLabel -> (Style[#, "Courier", Bold, 16] & /@
    {x, Overscript[x, "."]}),
 AspectRatio -> 1,
 PlotStyle -> {{Red, AbsoluteThickness[2]}}]
ParametricPlot[
 Evaluate[{t, x[t] /. sol}],
 {t, 0, 10},
 Frame -> True,
 Axes -> False,
 FrameLabel -> (Style[#, "Courier", Bold, 16] & /@
    {t, x}),
 AspectRatio -> .5,
 PlotStyle -> {{Green, AbsoluteThickness[3]}}]


Bob Hanlon


On Tue, Mar 5, 2013 at 10:14 PM, Rahul Chakraborty
<rahul.6sept at gmail.com> wrote:
> Dear all,
>
>  Following differential equation seems to have some error in coding by me. kindly let me know where i have gone wrong.
>
> Clear[x];
>  \[Omega]:=-2;
> eqn=x''[t]+ Sin  x[t]-\[Omega]^2  Sin  x[t]Cos  x[t]==0//Simplify;
> sol=NDSolve[{eqn,x[0]==1/2,x'[0]==0},x[t],{t,0,1000}][[1]]
> ParametricPlot[Evaluate[{x[t]/.sol,D[x[t]/.sol,t]}],{t,0,25},Frame->True,AxesLabel->{"x",Overscript[x,"."]},AspectRatio->1,PlotStyle->{{Red,AbsoluteThickness[2]}},TextStyle->{FontFamily->"Courier",FontWeight->"Bold",FontSize->16}]
> ParametricPlot[Evaluate[{t,x[t]/.sol}],{t,0,10},Frame->True,AxesLabel->{"t","x"},AspectRatio->.5,PlotStyle->{{Green,AbsoluteThickness[3]}},TextStyle->{FontFamily->"Courier",FontWeight->"Bold",FontSize->16}]
>
> Regards,
>
>  rahul
>

• References:
  • Problem in solving Differential Equation
    • From: Rahul Chakraborty <rahul.6sept@gmail.com>