# Help solving Homo ODE

by Konig
Tags: homogeneous, ode
 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
 P: 1,644 What, he didn't give you an easy one huh? But isn't the integrating factor x^(-a) so that you get: $$d(yx^{-a})=\frac{b}{x^{1+a}(1-x)^2}$$ Now suppose all you had to do was: $$\int \frac{b}{x^{1+a}(1-x)^2}dx$$ 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?
 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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