consider the differential equation
(x-1) squared y''+(1/x)y'-2y=0
find all the singular points of the equation and determine whether they are regular or essential singularities.
hence, explain why a solution of the form y= sigma (from j=0 to infinity) a (subscript j) x (to the power of j+k) should exist
The Attempt at a Solution
i found all the singular points but i dont see how thats going to help me determine why a solution of that form exists. usually doesnt one just ASSUME that a solution of that form exists?
thanks in advance