Re: How to Scale and vary plot for a Differential Equation
- To: mathgroup at smc.vnet.net
- Subject: [mg127383] Re: How to Scale and vary plot for a Differential Equation
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Fri, 20 Jul 2012 23:40:40 -0400 (EDT)
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You appear to be confusing the syntax of DSolve with that of NDSolve. DSolve can be used to solve the DE once rather than repeatedly inside the manipulate. DSolve[{x'[t] - r x[t] (1 - x[t]/K) == 0, x[0] == 1/2}, x[t], t][[1]] // Quiet {x[t] -> (E^(r*t)*K)/(-1 + E^(r*t) + 2*K)} Manipulate[ Module[{sol}, sol = {x[t] -> (E^(r*t)*K)/(-1 + E^(r*t) + 2*K)}; ParametricPlot[ Evaluate[{ x[t] /. sol, Log[D[x[t] /. sol, t]]}], {t, 0, 50}, Frame -> True, Axes -> False, FrameLabel -> {"x", Log[Overscript[x, "."]]}, AspectRatio -> 1, PlotRange -> {{0, 5.1}, {-6, 2.1}}]], {{r, 1}, 1, 5, 0.01, Appearance -> "Labeled"}, {{K, 1}, 1, 5, 0.01, Appearance -> "Labeled"}] Bob Hanlon On Fri, Jul 20, 2012 at 3:48 AM, Rahul Chakraborty <rahul.6sept at gmail.com> wrote: > Dear all, > > Kindly guide me for the above mentioned subject. I did try to code it but needs guidance.The code as below > > Clear[x]; > k[x_]=Manipulate[DynamicModule[{r:=1,K:=1},{Slider[Dynamic[r]],Slider[Dynamic[K]]},eqn=x'[t]-r x[t] (1-x[t]/K)==0//Quiet,sol=First@DSolve[{eqn,x[0]==1/2},x[t],{t,0,50}],[ParametricPlot[Evaluate[{x[t]/.sol,D[x[t]/.sol,t]}],{t,0,50},Frame->True,AxesLabel->{"x",Overscript[x,"."]},AspectRatio->1],ImageSize-> Scaled[r,K]],{r,1,5},{K,1,5},Initialization:> {r:=1,K:=1},SaveDefinitions-> True]] > > Regards, > rahul >
- References:
- How to Scale and vary plot for a Differential Equation
- From: Rahul Chakraborty <rahul.6sept@gmail.com>
- How to Scale and vary plot for a Differential Equation