Thread: Series solution about a singular point--help with y(2)

The given equation is x(x-1)y'' + 3y' - 2y = 0.

I was able to discern that a(k+1) = a(k) * [(k+r)(k+r-1)-2]/[(k+r+1)(k+r-3)], and the roots are 0 and 4. That recursive equation gives me the correct coefficients for a(0) through a(3), and of course, a(4) is undefined. But I can't get it right from a(5) on. I used the root 0 to get those first few a's; was I supposed to switch over to 4?

Regard the coefficient from the case as being arbitrary and then calculate the remaining coefficients in terms of
That gets you a solution containing two arbitrary constants, and in which case you have the general solution of the differential equation.
If you generate the series based on you will find that it duplicates the second part of the solution

Oh goodness--I made the remaining terms in terms of a(5), not a(4). Changing that fixed the problem.