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I would like to solve this differential equation and I am looking for the technique/answer

Consider a function $f=f(r)$

The differential equation is $$ f'' + (a(r^{-1})-b)f'+(c(r^{-2})+d(r^{-1}))f=0. $$ Boundary conditions $f(r=0)=0$ and $f(r=\infty)=0$.

Please help.

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This one looks ripe for a Frobenius type solution. – Ron Gordon Jan 17 '13 at 22:48
    
The frobenius solution is crazy and very messy. My guess is maybe this is a sturm louiville problem? I tried LaPlace/Fourier transforms but I didn't find a solution. – Joe Ganser Jan 18 '13 at 1:54
    
Also, Frobenius leads to a 3 term recursion relation. – Joe Ganser Jan 18 '13 at 2:01

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