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Series Solutions to a 2nd Order Diff. Eq.

  1. Jul 15, 2015 #1
    1. The problem statement, all variables and given/known data

    y'' + y' + xy = 0

    Just want to make sure I understand this completely, I had a bit of trouble towards the end, and thought the -29/600 was a little weird of a fraction to be right. I wasn't given a correct answer to base mine off, so I'm not sure if I'm doing this all right.

    2. Relevant equations



    3. The attempt at a solution

    upload_2015-7-15_19-19-23.png
     
  2. jcsd
  3. Jul 15, 2015 #2

    fzero

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    First off, you should always be able to verify that the solution you've derived is actually a solution by plugging it back into the DE and comparing terms order by order. Second, and more directly relevant, in your 5th line, you have lost the factor of ##x## in the 3rd, ##xy## term. Correcting this will significantly change the recursion relations.
     
  4. Jul 15, 2015 #3

    FactChecker

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    I think you forgot to increase the exponent of x in the last summation of line 5 when you multiplied through by x.
    Already answered above. How come I can't delete this?
     
  5. Jul 15, 2015 #4
    Thank you both, I will rework it and post my answer here.
     
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