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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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• References: <20120720074852.62B9B685F@smc.vnet.net>

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>