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Series solutions for differential equation

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Use the power series to solve the following differential equations, state the first four terms of the two independent solutions.

    3xy'' + y' - y = 0

    2. Relevant equations

    The power series.

    3. The attempt at a solution

    f1mpg0.png

    How do I get two independent solutions out of this? All of my coefficients will depend on the first a...?
     
    Last edited: Nov 15, 2012
  2. jcsd
  3. Nov 15, 2012 #2

    Dick

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    Your differential equation is singular at x=0. There are two solutions but one of them is singular at x=0. Your power series solution will only pick up the nonsingular one.
     
  4. Nov 15, 2012 #3
    Ah ok, so the problem is screwed up from the beginning, thanks :)
     
  5. Nov 15, 2012 #4
    Search for the form of the series solution near a regular singular point.
     
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