Re: [Q] Differential equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg22654] Re: [mg22620] [Q] Differential equation?
- From: "Henry Foley" <thomas_aq2 at email.msn.com>
- Date: Thu, 16 Mar 2000 09:11:11 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
James:
These were your equations -
y'_0(t) = -a * y_0(t) + b * y_1(t)
y'_1(t) = a * y_0(t) + (c*t-b) * y_1(t) --- (*)
Interesting - what is the physical system that they describe? Can you tell
us?
You do not need all the extraneous symbols. You can recast them as follows.
DSolve[
{y1'[t] == -a y1[t] + b y2[t], y2'[t] == a y1[t] + (c t - b)y2[t]},
{y1[t], y2[t]}, t]
However - this does not lead to a symbollic solution as you pointed out. (If
you can make ordering arguments that allow you to drop a term in the second
equation, such as y1[t], then it is soluble. No surprise!)
You can solve the problem numerically and I have included code below that
does this nicely. I used quite uncreative values for the parameters and
intial values. You could non-dimensionalize, i.e. normalize the parameters
and variables, then solve at specific ratio values of the parameters. At any
rate they are seemingly simple to solve numerically as follows:
a = 1;
b = 2;
c = 3;
a = NDSolve[
{y1'[t] == -a y1[t] + b y2[t],
y2'[t] == a y1[t] + (c t - b)y2[t],
y1[0] == 1, y2[0] == 1},
{y1[t], y2[t]}, {t, 0, 1}];
yy1[t_] := Evaluate[y1[t] /. a]
yy2[t_] := Evaluate[y2[t] /. a]
Plot[{yy1[t], yy2[t]}, {t, 0, 1}]
Peace!
Hank Foley
-----Original Message-----
From: James <research at proton.csl.uiuc.edu>
To: mathgroup at smc.vnet.net
Subject: [mg22654] [mg22620] [Q] Differential equation?
>
>Hi!
>
>I began to use Mathematica, and found out it is great.
>But I happen to have a question during solving differential equtations.
>Here's a problem.
>
> y'_0(t) = -a * y_0(t) + b * y_1(t)
> y'_1(t) = a * y_0(t) + (c*t-b) * y_1(t) --- (*)
> ^
>This can be solvable mathematically, even some tedious work,
>but when I use Mathematica, it can't solve it.
>After some trial and error, I found out that 't' in (*)
>is the problem - problem that mathematica doesn't give an answer,
>it just shows the above equations as an answer.
>So I wonder if this is the limit of Mathematica,
>or is there any way to solve it?
>I sincerely hope there's some way - because my work involves
>a lot of Diffrential Equations.
>Any reply would be appreciated.
>
>
>James.
>
>