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Re: Differential Equation: Not getting result

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  • Subject: [mg127335] Re: Differential Equation: Not getting result
  • From: Murray Eisenberg <murray at>
  • Date: Wed, 18 Jul 2012 01:37:11 -0400 (EDT)
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  • Reply-to: murray at

First, it's hard to help you when you _still_ have not learned basic 
Mathematica syntax. Did you, for example, look at examples for DSolve or 
NDSolve to see how you denote the derivative? It should be


and NOT (x^')[t].

Next, there is no need for NDSolve here, as the differential equation 
can be solved exactly (symbolically):

    r = 1; K = 1;
    eqn = x'[t] - r x[t] (1 - x[t]/K) == 0

    DSolve[eqn, x[t], t]

The result, in InputForm, is:

    {{x[t] -> E^t/(E^t + E^C[1])}}

(Did you try that? If not, why not??)

(Of course that is a "generic" solution, depending on ONE parameter 
C[1], that does not include the trivial solution identically zero.)

Next, look at the first initial condition you want, x[0] == 1/2.

    DSolve[{eqn, x[0] == 1/2}, x[t], t]

The result, again in InputForm, is:

    {{x[t] -> E^t/(1 + E^t)}}

(You'll see a DSolve warning there about inverse functions.)

So you cannot possibly expect to satisfy your additional condition 
x'[0]==0 as well. In fact, if you try it...

    DSolve[{eqn, x[0] == 1/2, x'[0] == 0}, x[t], t]

... then you get an empty solution set!

Going back to just one initial condition, for x[0]...

    sol = First @ DSolve[{eqn, x[0] == 1/2}, x[t], t]

... you'll get a plot from:

   ParametricPlot[Evaluate[{x[t] /. sol, D[x[t] /. sol, t]}], {t, 0, 50}]

Finally, suppose you really did want, for reasons unknown, to use 
NDSolve instead of solve. Still, you cannot use both initial conditions, 
just the first.

On 7/17/12 1:31 AM, Rahul Chakraborty wrote:
> Dear all,
>   For the following code i'm not getting result. kindly tell me where i'm making mistake.
> Clear[x];
> r=1;
> K=1;
> eqn= (x^')[t]-r  x[t]  (1-x[t]/K)==0//Simplify;
> sol=NDSolve[{eqn,x[0]==1/2,x'[0]==0},x[t],{t,0,50}][[1]]
> ParametricPlot[Evaluate[{x[t]/.sol,D[x[t]/.sol,t]}],{t,0,50},Frame->True,AxesLabel->{"x",Overscript[x,"."]},AspectRatio->1]
> ParametricPlot[Evaluate[{t,x[t]/.sol}],{t,0,50},Frame->True,AxesLabel->{"t","x"},AspectRatio->1]
> Regards,
> rc

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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