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Homework Help: Series solution for differential equation

  1. Dec 15, 2016 #1
    <OP warned about not using the homework template>

    Obtain a series solution of the differential equation x(x − 1)y" + [5x − 1]y' + 4y = 0

    Do I start by solving it normally then getting a series for the solution or assume y=power series differentiate then add up the series?

    I did the latter and got three different but (slightly similar) looking series and the problem asks to group them all into one series which I cannot do
    Last edited by a moderator: Dec 15, 2016
  2. jcsd
  3. Dec 16, 2016 #2


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    You have a series for y, e.g. ##y = \displaystyle \sum_{n=0}^\infty c_nx^n## so that $$y' = \sum_{n=1}^\infty n c_nx^{n-1}\quad{\rm {and}}\quad y'' = \sum_{n=2}^\infty n (n-1) c_nx^{n-2} \ , $$ right ?

    Now work out the coefficient of ##\ x^n ## in x(x − 1)y" + [5x − 1]y' + 4y = 0
    Last edited: Dec 18, 2016
  4. Dec 17, 2016 #3


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    What's stopping you?
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