Help solving Homo ODE


by Konig
Tags: homogeneous, ode
Konig
Konig is offline
#1
Nov13-11, 09:48 AM
P: 6
Hi, need help solving a first order homogeneous ODE.

y'(x)-(a/x)y = b/(x(1+x)^2) Here a and b are some constants.

Need to solve this for y.

My attempts so far have been to use



But this means solving ∫ x^(-a)/(x(1+x)^2) dx which has solutions in terms of Gauss hyper-geometric functions,

http://en.wikipedia.org/wiki/Hypergeometric_function

Which lead me to believe i'm going wrong somewhere....

Sorry for the maths format, i'm new to here and don't know how to insert LaTeX.

Thanks
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jackmell
jackmell is offline
#2
Nov13-11, 12:29 PM
P: 1,666
What, he didn't give you an easy one huh? But isn't the integrating factor x^(-a) so that you get:

[tex]d(yx^{-a})=\frac{b}{x^{1+a}(1-x)^2}[/tex]

Now suppose all you had to do was:

[tex]\int \frac{b}{x^{1+a}(1-x)^2}dx[/tex]

Could you use parts say, one, two, three, four times, look at what's happening to the sequence, then come up with a general (infinite-term) expression for the solution that when you checked out the power-series expression for the Hypergeometric series solution reported by Mathematica, the series you get looks like it?
Konig
Konig is offline
#3
Nov14-11, 03:12 PM
P: 6
thanks for the response Jackmell,

Am currently working on it, though keep making maths errors which are slowing me down.

I agree it would be a good idea to compare, thanks for the tip.

The problem is part of a project, so yea the problems not meant to be easy.
demoralising thing though is that i'm not sure i was supposed to take this long with it!

Konig


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