Re: [Q] Differential equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg22656] Re: [mg22620] [Q] Differential equation?
- From: "Tomas Garza" <tgarza at mail.internet.com.mx>
- Date: Thu, 16 Mar 2000 09:11:13 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
James [research at proton.csl.uiuc.edu] wrote:
> 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.
There are a couple of things you might consider, to start with:
1. The blank character "_" has a specific meaning in Mathematica:" _ or
Blank[ ] is a pattern object that can stand for any Mathematica expression"
cf. Help Browser or The Book. If, as I presume, you are using it to
distinguish between two functions, try changing the names of those
functions, e.g., y instead of y_0, and x instead of y_1.
2. I expect you are using [ and ] instead of ( and ) in your Mathematica
code, as well as "==" instead of "=".
Just to give you a taste of Mathematica's capabilities, try using DSolve
setting all your constant terms a, b, c equal to 1:
In[1]:=
DSolve[{y'[t] == y[t] + x[t],
x'[t] == y[t] + t *x[t]}, {x[t], y[t]}, t]
I omit the rather lengthy output. The solutions are given in terms of
transformation rules (that's the way it goes with Mathematica):
{x[t] -> "something", y[t] -> "somethingelse"}
You may then simplify to see what happens. For the sake of expediency,
simply copy and paste "something" and "somethingelse" and write
"something"//Simplify
"somethingelse"//Simplify
and you'll get nice and clean expressions for x[t] and y[t] with two
constants c[1] and c[2] which must be determined from boundary conditions.
Tomas Garza
Mexico City