Help with solving ode

1. Oct 16, 2013

bart007

1. The problem statement, all variables and given/known data
Using method of frobenius about $x=0$ to solve:
$(1-x) y''+xy'-\frac{\alpha^2}{x^2}+=0$


2. Relevant equations
N/A

3. The attempt at a solution
1. plug in series in to the equation.
2. adjust the index off all the terms.
3. write the extra terms separately so that we have all series starting at the same point.

and I get...

that the roots from the indicial equation
$\lambda=\frac{1}{2}(1\pm\sqrt{4a^2+1})$
and for the recursion I get
$c_n=\frac{c_{n-1}(\lambda+n-1)(\lambda+n-2)-c_{n-2}(\lambda+n-2)}{(\lambda+k)(\lambda+n-1)-\alpha^2}$

I am not sure how to check if this is correct or not.
Using a number for $\alpha$ I don't get any nice series that has a function.

2. Oct 16, 2013

bart007

Sorry for the double post, first post was not showing.