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Nonlinear diff equation and power series

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data

    i need to solve this diff equation.

    y' = x2 + y2

    y = 1 when x = 0

    i can assume that the answer is a power series on the form Ʃanxn

    andi only need the 4 first non zero terms of the power-series answer


    2. Relevant equations

    Ʃanxn

    3. The attempt at a solution

    y = Ʃanxn
    y' = Ʃnanx(n-1)

    Ʃn*anx(n-1) - (Ʃanxn)2 = x2

    i guess since the answer is only 4 first non zero term. i can write out the summation to 4 terms.

    if i do that im stuck with a bunch of a1 a2 a3 .... and i cant mange to find the value of those coefficients. and i dont really know if that is the right way of doing it at all.
     
  2. jcsd
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