I am trying to solve y''+(3-1/x^2)y=0. Is it possible to solve by separation? Or will this require a series solution?
If by "separation" you mean writing it as and then to
, then, no, you cannot "separate" a second order derivative like you can a first order derivative. The "differentials" dy and dx are defined in Calculus, but such things as " " and " " are NOT defined.