Special Second Order Ordinary Diff. Equation

[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??

 

[SteamKing]

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??

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

 

[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??

 

[SteamKing]

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??

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