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Radius of convergence question

  1. Feb 22, 2009 #1
    1. The problem statement, all variables and given/known data
    What feature of the ODE explains your value for the radius of convergence of the series y2?
    y2 is a series which satisfies the ODE and I found that it converges for [tex]\abs{2x^2} < 1[/tex].

    2. Relevant equations
    [tex]y2=x-\frac{2}{3}x^2-\frac{4}{15}x^5+ \cdots[/tex]

    ODE: [tex](1-2x^2)\frac{d^2y}{dx^2} +4y = 0[/tex]

    3. The attempt at a solution
    I presume this has something to do with the [tex](1-2x^2)[/tex] in the ODE but I'm not sure. Can someone help?
  2. jcsd
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