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*Delivered-to*: mathgroup-newsend@smc.vnet.net*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[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>