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Re: Problem in solving Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg130239] Re: Problem in solving Differential Equation
• From: Rahul Chakraborty <rahul.6sept at gmail.com>
• Date: Thu, 28 Mar 2013 04:05:38 -0400 (EDT)
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• References: <20130306031441.3FE5E665F@smc.vnet.net>

Sir,

 Can you kindly see what is the mistake in this code of mine. Its not
giving me the output.


 Clear [x,t];
eqn=x'[t]+lambda*x[t]==0;
Manipulate[[sol_]=NDSolve[{eqn,x[0]==1/2},x[t],{t,0,50}][[1]];
ParametricPlot[Evaluate[{x[t]/.sol,D[x[t]/.sol,t]}],{t,0,25},PlotRange->{{-20,20},{-25,25}},Frame->True,Axes->False,FrameLabel->(Style[#,"Courier",Bold,16]&/@{"x",Overscript[x,"."]}),AspectRatio->1,PlotStyle->{{Red,AbsoluteThickness[2]}}],{{lambda,0.5},0,5}]



Sincerely,

 Rahul

On 3/6/13, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> 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>