Re: Help DSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg39146] Re: Help DSolve
- From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
- Date: Fri, 31 Jan 2003 04:37:05 -0500 (EST)
- References: <b1afku$pg9$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This appears to make my copy of Mathematica 4.2 hang. So we have to hep
things along a bit by hand.
Solve the homogeneous differential equation (i.e. r.h.s.=0) thus:
DSolve[{(1 + x)y''[x] - 2(x + 2)y'[x] + 4y[x] == 0}, y, x]
Use linear combinations of these two solutions to construct the Green's
function which solves the inhomogeneous equation (1 + x)y''[x] - 2(x +
2)y'[x] + 4y[x] == DiracDelta[x-a]. On either side of the point x=a the
Green's function is a (different) linear combination of the solutions of the
homogeneous differential equation (this is all standard stuff you can find
in textbooks). Once you have the Green's function you can find the solution
to the inhomogeneous differential equation for any r.h.s. Mathematica will
help you do the integrals that occur when you compute the solution by this
route.
--
Steve Luttrell
West Malvern, UK
"gianpf" <Jean.Pellegri at wanadoo.fr> wrote in message
news:b1afku$pg9$1 at smc.vnet.net...
> I want to solve :
>
> (1+x)y''[x]-2(x+2)y'[x]+4y[x) == x
>
> Could someone can find a way out for this ?
>
> Thanks.
>