How to solve second order linear differential equations with non-constant coefficients

Article View: sci.math.num-analysis.sci.math

Article #1

Back to sci.math.num-analysis.sci.math Previous Next

From: posenj
Date: Sat, 02 May 1998 00:00

30 lines
1417 bytes

Hi.

This isn't covered in my math syllabus at university. We've used
D-operators and other methods to solve the following type of d.e.:

a.y''(t) + b.y'(t) + c.y(t) = s(t)

where a, b, c are constant.

But how do you solve

f(t).y''(t) + g(t).y'(t) + h(t).y(t) = s(t)

where f, g, h are not constant. I'm interested mainly in numerical
approximation.

I've tried substituting u(t) = y'(t) and then I get two equations:

1)	du = (s/f).dt - (g/f).u.dt - (h/f).y.dt
2)	u = dy/dt

And, although it look slike I'm getting somewhere, I'm not sure where
to go from there.

Any ideas?

Thanks,
Kevin Posen
South Africa

Technical Details

Message-ID: <354b90c1.1170824@news.saix.net>

Path: arc1-ca.pugleaf.net!unknown!not-for-mail

Show Full Headers

Complete Article Headers

X-Google-Language: ENGLISH,ASCII-7-bit
X-Google-Thread: 1130d6,bb26432a4748c7a3,start
X-Google-Attributes: gid1130d6,public
X-Google-Thread: 146d2e,bb26432a4748c7a3,start
X-Google-Attributes: gid146d2e,public
X-Google-Thread: 10d67e,bb26432a4748c7a3,start
X-Google-Attributes: gid10d67e,public
From: posenj@lancet.co.za
Subject: How to solve second order linear differential equations with non-constant coefficients
Date: 1998/05/02
Message-ID: <354b90c1.1170824@news.saix.net>
X-Deja-AN: 349792018
Content-Transfer-Encoding: 7bit
Content-Type: text/plain; charset=us-ascii
Organization: The South African Internet Exchange.
Mime-Version: 1.0
Reply-To: posenj@lancet.co.za
Newsgroups: sci.math.num-analysis.sci.math,aus.mathematics,alt.math.recreational