
#1
Nov1311, 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 hypergeometric 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 



#2
Nov1311, 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}(1x)^2}[/tex] Now suppose all you had to do was: [tex]\int \frac{b}{x^{1+a}(1x)^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 (infiniteterm) expression for the solution that when you checked out the powerseries expression for the Hypergeometric series solution reported by Mathematica, the series you get looks like it? 



#3
Nov1411, 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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