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Math Help - Easy Question

  1. #1
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    Easy Question

    (x^2+2)y'' + 2xy' = 0

    Verify x=0 is an ordinary point. Then find a lower bound for the radius of convergence of power series solutions about x=0
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  2. #2
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    Quote Originally Posted by Creebe View Post
    (x^2+2)y'' + 2xy' = 0

    Verify x=0 is an ordinary point. Then find a lower bound for the radius of convergence of power series solutions about x=0
    If you put it in standard form you get

    y'' +\frac{2x}{x^2+2}y'=0

    Since the limit as \lim_{x \to 0}\frac{2x}{x^2+2}=0 is finite it is an ordinary point.


    The power series will have radius of convergence of at least the distance to the nearest singularity in the complex plane.

    x^2+2=0 \iff x \pm i\sqrt{2}

    So the radius of convergence of at least R=\sqrt{2}
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