Re: [Q] Differential equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg22633] Re: [mg22620] [Q] Differential equation?
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Thu, 16 Mar 2000 09:10:49 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
James,
I tried solving your eqns and got the same result -- mathematica just
returns the input line DSolve[ {...., ....},{y0[t],y1[t]},t ]. Inspecting
the equations, I noticed that there are some dependencies between them --
the sum of the 2 eqns, y0'[t]-y1'[t] == b y1[t] - (c t -b) y1[t] doesn't
involve y0[t] at all! Also, what if c=0? So I changed the equations
somewhat
a=2; b=1; c=3; d=4;
eqns2= {y0'[t] == -a * y0[t] + b * y1[t], y1'[t] == c * y0[t] + (2*t-d) *
y1[t] };
so that the matrix of the equations is full-rank. Now
DSolve[eqns2,{y0[t],y1[t]},t]
returns something so ugly, I won't try to print it; but it looks like
expressions for y0 and y1 in terms of integrating factors that are
exponentials of integrals of expressions in Bessel I functions (try it
yourself). At least, its a solution. I know mathematica is very fussy
about returning solutions requiring unstated assumptions to be valid, and I
think that is part of your problem. Try defining the problem a little more
carefully, and it may be that if the coefficients of y0[t] have to be
negatives of each other, then the equations are not soluble.
-mark
-----Original Message-----
From: James <research at proton.csl.uiuc.edu>
To: mathgroup at smc.vnet.net
Subject: [mg22633] [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.
>
>