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Special Second Order Ordinary Diff. Equation

  1. Jan 26, 2016 #1
    Hello guys, i'm studying from Green's Function With Applications by Duff, and he finds the general solution(homogeneous sol.) to this differential equation: BBg5D4l.png , but i i've never seen a equation like this before, how can i manage to solve this equation??
     
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  3. Jan 26, 2016 #2

    SteamKing

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    It depends on what P is. I assume that k is a constant. Otherwise, you have a fourth-order, non-homogeneous ODE.
     
  4. Jan 26, 2016 #3
    P is only function of x, and k is indeed a constant, but i'm trying to solve the homogeneous eqn, that it's part of constructing the green function of this equation, how i solve the homogeneous one??
     
  5. Jan 26, 2016 #4

    SteamKing

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    If P is a function of x, what sort of function is it? The general method of solution to these types of ODEs is by infinite series.

    http://tutorial.math.lamar.edu/Classes/DE/SeriesIntro.aspx
     
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