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## Homework Statement

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