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MathGroup Archive 2005

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Re: 'Changing' parameters in an expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60570] Re: 'Changing' parameters in an expression
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Tue, 20 Sep 2005 05:20:10 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 9/19/05 at 4:45 AM, anonmous69 at netscape.net (Matt) wrote:

>What follows (at the end) worked for me, however, I'm wondering if
>it's the 'right' approach or not.  What I mean by 'right' is this: 
>my eventual approach worked, but there may be another approach that
>is more efficient and demonstrates a more wide ranging principal in
>using Mathematica, and hence would be applicable in many
>situations.

>I started off with this: eqn = x'[t] == x[t](x[t] - a);

>(I am using eqn as the first argument to DSolve, which is why it
>appears as it does.)

>I wanted to plot the rhs of eqn with 'a' having a value of 1/2, so
>first I tried this: Plot[eqn[[2]] /. a->1/2, {t, 0, 6}];

>That didn't work as I got these types of errors:

It doesn't work because the function x is undefined. You are asking Plot to handle x[t](x[t]-1/2). You told plot to sample this from t=0 to t=6, But you haven't told Mathematica how to compute x[t].

>I tried a few other rules with essentially the same results and
>then I tried this: Plot[eqn[[2]] /. {a->1/2, x[t]->x}, {x, 0, 6}];

Now you have changed the function to a polynomial in x and asked for the polynomial to be plotted from 0 to 6. Mathematica now has all the information needed to create the plot.

>Which worked for me.  I'm sure it has something to do with what I'm
>asking Plot to work with.  It just seems strange to me that DSolve
>will work with eqn, but Plot does not.

Why? DSolve is intended to find an unknown function that solves a differential equation. Plot is designed to plot a *known* function. These tasks are fundamentally different.
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