Special Second Order Ordinary Diff. Equation

1. Jan 26, 2016

Andreol263

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: , but i i've never seen a equation like this before, how can i manage to solve this equation??

2. Jan 26, 2016

SteamKing

Staff Emeritus
It depends on what P is. I assume that k is a constant. Otherwise, you have a fourth-order, non-homogeneous ODE.

3. Jan 26, 2016

Andreol263

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??

4. Jan 26, 2016

SteamKing

Staff Emeritus
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