       Re: How to Scale and vary plot for a Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg127404] Re: How to Scale and vary plot for a Differential Equation
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 22 Jul 2012 04:33:06 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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• References: <20120720074852.62B9B685F@smc.vnet.net>

```It is not required. If you don't like it, don't use it. Adjust
PlotRange to taste.

Bob Hanlon

On Sat, Jul 21, 2012 at 12:57 AM, Rahul Chakraborty
<rahul.6sept at gmail.com> wrote:
> Dear Bob,
>
>  Thanks.
>
> But one query, why it is required to use Log   in " Log[D[x[t] /. sol,
> t]". Because in simple plot without Manipulate it is not required.
>
>
>  Regards,
>  rc
>
> On 7/21/12, Bob Hanlon <hanlonr357 at gmail.com> wrote:
>> 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 == 1/2}, x[t], t][] // 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==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

```

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