```Date: Mar 28, 2013 5:12 PM
Author: Bob Hanlon
Subject: Re: Problem in solving Differential Equation

You have addressed different problems in this one thread and it isunclear to which problem you are currently having problems. You havenot provided any of your code so I cannot say why you are gettingerror messages. I obviously don't have a problem with the code that Isent.If you are putting multiple Manipulate statements in the same notebookthat use the same symbol names they are probably interacting with eachother. Use Module inside each Manipulate to constrain the scope ofdefinitions, or use different symbol names in the different Manipulatestatements.Bob HanlonOn Thu, Mar 28, 2013 at 4:06 AM, Rahul Chakraborty<rahul.6sept@gmail.com> wrote:> 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@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@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,Absolu=teThickness[2]}}],{{lambda,0.5},0,5}]>>>>>>>>>>>> Sincerely,>>>>>>  Rahul>>>>>> On 3/6/13, Bob Hanlon <hanlonr357@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@gmail.com> wrote:>>>>> Dear all,>>>>>>>>>>  Following differential equation seems to have some error in coding b=y>>>>> 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//Simpli=f=> 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->T=rue,AxesLabel->{"x",Overscript[x,"."]},AspectRatio->1,PlotStyle->{{Red,Abso=luteThickness[2]}},TextStyle->{FontFamily->"Courier",FontWeight->"Bold",Fon=tSize->16}]>>>>> ParametricPlot[Evaluate[{t,x[t]/.sol}],{t,0,10},Frame->True,AxesLabel=->{"t","x"},AspectRatio->.5,PlotStyle->{{Green,AbsoluteThickness[3]}},TextS=tyle->{FontFamily->"Courier",FontWeight->"Bold",FontSize->16}]>>>>>>>>>> Regards,>>>>>>>>>>  rahul>>>>>>>>>>>>
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