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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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