Second order diff. equation. Series solution

Hi there. I have to solve:

I thought I should use a series solution, but I'm not sure if what I'm doing is ok. So, I've considered

And

Then, using that m=n-2 for y'' and then replacing in the diff. eq:

So:

Then:

And:

Now I have to find the recurrence for

Is this ok?

Re: Second order diff. equation. Series solution

I think I should solve the homogeneus equation first.

Re: Second order diff. equation. Series solution

Re: Second order diff. equation. Series solution

Thanks, but I have to solve it using series.