This is a pretty general conceptual question. I was just doing some reviewing for a test, and it occurred to me that if I were not told specifically to use Frobenius method on an equation, I might try to Power series solve it and vice versa. Can we talk about the difference a bit? We apply both methods to the equation of the form: y'' + p(x)y' +q(x)y = 0 I know that using the Frobenius method has something to do with the fact that we can develop a solution about a regular singular point. But when would a power series solution fail where a Frobenius would not? It seems like we are taking a differential equation whose solution cannot be found due to singularities and forcing a solution from it by multiplying through by x2 and solving that equation instead. Any thoughts on this?