Re: Problem in solving Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg130241] Re: Problem in solving Differential Equation
• From: Rahul Chakraborty <rahul.6sept at gmail.com>
• Date: Thu, 28 Mar 2013 04:06:19 -0400 (EDT)
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• References: <20130306031441.3FE5E665F@smc.vnet.net>

```Sir,

Its  not giving output. The following error its showing

ERROR: Set::write: : Tag List in {150 Cos[15 t]+5.` Sin[15
t]==0,False}[t_] is Protected.

DSolve::dsfun: "10\ Sin[15\ t] cannot be used as a function."

ReplaceAll::reps: "{150\ Cos[15\ t]+5.\ Sin[15\ t]==0,False} is
neither a list of replacement rules nor a valid dispatch table, and so
cannot be used for replacing"

These ERROR messages are coming repeatedly.

Regards,

Rahul

On 3/28/13, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> Your DE can be solved exactly using DSolve.
>
> Manipulate[
>  eqn = x'[t] + lambda*x[t] == 0;
>  sol[t_] = x[t] /. DSolve[
>      {eqn, x[0] == 1/2}, x[t], t][[1]];
>  ParametricPlot[
>   {sol[t], sol'[t]},
>   {t, 0, 25},
>   PlotRange -> {{-0.1, 0.6}, {-3, 0.5}},
>   Frame -> True,
>   Axes -> False,
>   FrameLabel -> (Style[#, "Courier", Bold, 16] & /@
>      {x, Overscript[x, "."]}),
>   AspectRatio -> 1,
>   PlotStyle -> {{Red, AbsoluteThickness[2]}}],
>  {{lambda, 0.5}, 0, 5, 0.01, Appearance -> "Labeled"}]
>
>
> Bob Hanlon
>
>
> On Wed, Mar 27, 2013 at 11:29 PM, Rahul Chakraborty
> <rahul.6sept at gmail.com> wrote:
>> 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//Simplif=
y;
>>>> 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
>>>>
>>>
>

```

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