Question on series solutions of diff equations

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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 don't see how that's going to help me determine why a solution of that form exists. usually doesn't one just ASSUME that a solution of that form exists?
thanks in advance

 

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hey r people not answering my question cos they r as clueless as i am or cos i somehow annoyed you by not typing out the subscripts properly? i don't know how to do that