I know the solution now... so no need to answer now, this one is correct.
I'm supposed to solve differential equation:
by Frobenius method.
The first solution is , where is a constant. I am not sure if the second solution is correct. I got:
or if I put it in the sum:
So, please if someone could check and tell me if this is OK. If not, I would appreciate if you could write the procedure how you got the second solution different from mine.