From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Subject: Re: diff. equation
Date: 21 Jan 2000 07:53:00 GMT
Newsgroups: sci.math
Summary: [missing]

In article <VuJh4.179$VH3.44324@news1.atlantic.net>, cpei <cpei@fdn.net> wrote:
>please help to solve following diff. eq.:
>dy/dt=3+2y-4x
>dx/dt=f(t)*(3y+2x)
>f(t)=1/(4+5t)

Use the first to solve for  x; then you have a single second-order linear
ODE to solve for  y = y(t). The constant function  y(t)=-3/8  is a solution;
add to this any solution of the homogeneous equation
(4+5t) y'' - 10(1+t) y' + 16 y = 0. Maple reports two linearly independent
solutions to this to be    hypergeom([-8/5],[-2/5],2*t+8/5)      and
2/625*(4+5*t)*(5000+6250*t)^(3/5)*hypergeom([-8/5, -1/5],[],-5/2/(4+5*t)) .
Charming, huh?

dave