Re: Problem in solving nonlinear Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg128314] Re: Problem in solving nonlinear Differential Equation
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Sat, 6 Oct 2012 01:51:12 -0400 (EDT)
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• References: <k4lvgc\$d3j\$1@smc.vnet.net>

```Am 05.10.2012 08:42, schrieb Rahul Chakraborty:
> 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}]

The message "x appears with no arguments" points to the expression
"x^3[t]. Replace it by x[t]^3.  The direct power of functions is not
defined in Mathematica. Using function composition notations one had to
use complicated expressions like Power[x[#],3]&[t]

--

Roland Franzius

```

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