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Homework Help: Analytic solution?

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider the following ODE
    [tex] x^3y' - 2y + 2x = 0 [/tex]

    2. Relevant equations
    Prove that the ODE has no analytic solution in any neighborhood of [tex] x=0 [/tex].

    3. The attempt at a solution
    Its general solution is [tex]Ce^{-\frac{1}{x^2}}+ e^{-\\frac{1}{x^2}} \int_{x_0}^x - \frac{2e^{\frac{1}{t^2}}}{t^2} dt [/tex] which is not continuous in [tex]x=0[/tex], but I don't think this is unique so I don't know if it helps. Should I try to substitute an arbitrary power series in the equation?
     
  2. jcsd
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