From: harper@kauri.vuw.ac.nz (John Harper)
Newsgroups: sci.math.num-analysis,comp.soft-sys.matlab
Subject: Re: Solution to a differential equation
Date: 3 Dec 1998 01:27:43 GMT

In article <36659BB3.BDEE144C@are1.cals.ncsu.edu>,
Paul Fackler  <paul_fackler@ncsu.edu> wrote:
>Does anyone know offhand the general solution to the following ODE:
>y''(x)=ay(x)+(b+cx)y'(x)?
>I'm sure it's relatively simple but can't dredge it up.

Start by putting t = k(b+cx), y(x) = f(t) where k is a constant, to 
get f'' + 2tf' - 2nf = 0. If n is an integer there is a solution in 
terms of integrals or derivatives of error functions (Abramowitz & 
Stegun Handbook Math. Functions p299). If not, p300 would make me 
try parabolic cylinder functions if it was my problem. The standard 
reference on this sort of thing is Kamke, Differentialgleichungen 
Losungsmethoden und Solutionen (Chelsea, NY 1948 reprinting the 
original German ed. Don't worry if you can't read German: reading 
the mathematics will give you what you need.)

John Harper, School of Mathematical and Computing Sciences, 
Victoria University, Wellington, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)471 5341 fax (+64)(4)495 5045