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Series Solution ODE

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Obtain solution valid near x=0

    2. Relevant equations
    (x2+1)y''+6xy'+6y=0


    3. The attempt at a solution
    y"+6x/(x2+1)y'+6x/(x2+1)=0
    In representing the solution in series notation, I'm not sure how deal with the rational function because I know I need to have all of the x terms inside the summation and create powers of x that are all the same to create a single summation. The denominator of a rational function does not seperate, so how would adjust the summation to take this into account?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 20, 2010 #2

    vela

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    Substitute the series into the original equation, not the one with x2+1 in the denominators.

    (I'm not sure exactly what your question is, but I took a stab at what I thought you meant.)
     
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