Problem in solving nonlinear Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg128301] Problem in solving nonlinear Differential Equation
• From: Rahul Chakraborty <rahul.6sept at gmail.com>
• Date: Fri, 5 Oct 2012 02:52:27 -0400 (EDT)
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```Dear All,

I'm facing some problem in solving non-linear differential equation. I'm not getting output.The code as follows:

Clear[x,Q,\[CapitalGamma],\[Phi]];
Q:=100;
\[CapitalGamma]:=50;
Subscript[\[Omega], 0]:=10;
Subscript[V, p]:=1/2;
Subscript[C, 0]:=406 * 10^-6;
\[Phi]:=90;
\[Gamma]:=1/Q;
Subscript[V, 1][t]:=Sqrt[2] Subscript[V, p]Sin[2Subscript[\[Omega], 0]t];
Subscript[k, 3]:=5;
eqn= x''[t]+\[Gamma] Subscript[\[Omega], 0]x'[t]+Subscript[\[Omega], 0]^2 (1+Subscript[C, 0]Subscript[V, 1][t])x[t]-\[CapitalGamma] Sin[Subscript[\[Omega], 0]t+\[Phi]]+Subscript[k, 3](x^3)[t]==0//Simplify;
sol=NDSolve[{eqn,x[0]==1/2,x'[0]==0},x[t],{t,0,50}][[1]]
ParametricPlot[Evaluate[{x[t]/.sol,D[x[t]/.sol,t]}],{t,0,50},Frame->True,AxesLabel->{"x",Overscript[x,"."]},AspectRatio->1,PlotStyle->{{Red,AbsoluteThickness[1]}},TextStyle->{FontFamily->"Courier",FontWeight->"Bold",FontSize->16}]
ParametricPlot[Evaluate[{t,x[t]/.sol}],{t,0,50},Frame->True,AxesLabel->{"t","x"},AspectRatio->.5,PlotStyle->{{Green,AbsoluteThickness[1]}},TextStyle->{FontFamily->"Courier",FontWeight->"Bold",FontSize->16}]

Regards,

rahul

```

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