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Homework Help: Power series to solve 2nd order ordinary differential equations

  1. Oct 20, 2006 #1
    I need some help with power series.
    I can't remember how to find a power series center around a point.
    example question:
    y"-xy'-y=0, x=1
    I don't how to start this.
  2. jcsd
  3. Oct 20, 2006 #2


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    Homework Helper

    You should find this link useful: http://tutorial.math.lamar.edu/AllBrowsers/3401/SeriesSolutions.asp" [Broken].
    Last edited by a moderator: May 2, 2017
  4. Oct 20, 2006 #3
    Yes, thanks. The site has been helpful, but I have a question that I couldn't find an answer for. What happens if you have a summation with the starting index of the summation with n=0 but one of the summations you have an index of n=1. All the exponents are the same.

    Also what happens if instead x=1?
  5. Oct 20, 2006 #4
    If you start at n =1, you subtract 1 from the exponent. So:

    [tex] \sum_{n=0}^{k} x^{n} = \sum_{n=1}^{k}x^{n-1} [/tex]
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