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Series Solution around singular point

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    x(2 - x)y'' - (x - 1)y' + 2y = 0
    Find the general solution in terms of a polynomial and a series in powers of x - 1.

    2. Relevant equations

    3. The attempt at a solution
    Does the question basically ask for a series solution of the ODE at the regular point x = 1?
    Then [itex]y(x) = \sum^{∞}_{n = 0}c_{n}(x - 1)^{n}[/itex]
    If I sub that into the ODE then I get a rather complicated algebraic mess for x(2 - x)y''. Is this the right way to solve this?
  2. jcsd
  3. Jan 23, 2012 #2


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    Try changing variables from x to u=x-1. That'll simplify the algebra a bit.

    I don't see how you're going to get a polynomial solution. Did you type the DE as given?
    Last edited: Jan 23, 2012
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