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Solution to 2nd O.D.E. using power seris

  1. Aug 2, 2004 #1
    Can anyone show me a complete solution to the problem below using power series?

    y"+xy=x^2 y(0)=1 , y'(0)=0
     
  2. jcsd
  3. Aug 2, 2004 #2

    Galileo

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    Start with assuming a solution in the form of a power series:
    [tex]y=\sum_{n=0}^{\infty}a_nx^n[/tex]

    Plug it into your differential equation and simplify. I think you should get a recursive relation between your coefficients whose initial values [itex]a_0[/itex] and [itex]a_1[/itex] can be determined from your initial conditions.
     
    Last edited: Aug 2, 2004
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