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Math Help - Second order ODE with non-constant coefficients

  1. #1
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    Second order ODE with non-constant coefficients

    I am trying to solve y''+(3-1/x^2)y=0. Is it possible to solve by separation? Or will this require a series solution?
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    Re: Second order ODE with non-constant coefficients

    If by "separation" you mean writing it as \frac{d^2y}{dx^2}= (\frac{1}{x^2}- 3)y and then to
    \frac{d^2y}{y}= (\frac{1}{x^2}- 3)dx^2, then, no, you cannot "separate" a second order derivative like you can a first order derivative. The "differentials" dy and dx are defined in Calculus, but such things as " d^2y" and " dx^2" are NOT defined.
    Last edited by HallsofIvy; October 21st 2011 at 01:54 PM.
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    Re: Second order ODE with non-constant coefficients

    Quote Originally Posted by toobusy View Post
    I am trying to solve y''+(3-1/x^2)y=0. Is it possible to solve by separation? Or will this require a series solution?
    It's a homogeneous linear equation, and thus always has the zero solution. However, if you desire non-trivial solutions, then series is the way to go.
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    Re: Second order ODE with non-constant coefficients

    Thanks! I just figured it out!
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