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Another power series DE question

  1. Aug 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Using power series, find the solution to the following DE

    y" + xy' + y=0

    Given data xo = 0

    y(0)=1 and y'(0) = 1

    2. Relevant equations

    y(x) = [itex]\sum[/itex]an(x-xo)^n for n= 0 to [itex]\infty[/itex]

    3. The attempt at a solution

    Please see attached file. The part circled at the top is the answer the tutorial sheet gives.

    Im thinking I could have a conceptual problem. Please feel free to point any misunderstandings I may have made


    Attached Files:

  2. jcsd
  3. Aug 27, 2011 #2


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    When you reindex the first sum with n going to n+2, you need to change (n-1) to (n+1). In the y' term, you seem to have forgotten the coefficient x. It'll eliminate the need to reindex the second series. That in turn will fix your recurrence relation, hopefully.
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