Can somebody tell me what type is this differential equation:

 

y''-f(x)y'-sin(y + h(x))=0

 

I am interested more at numerical solution.

differential equations never have numerical values, at least as far as I know

 

 

other than that its a pde as far as I can tell

it wont have a numerical solution with 2 general functions of x in it as far as I can see... as for working it out, it's late and I'm tired and havn't done any seriouse maths for a couple months

I need only algoritam how too break this equation so I can solve it with runge-kutte metod. I forget to say that y=y(x).

The sin(y + h(x)) is problem. It is not a polinom but... maybe I can transform it in sum so sin become a polinome.

PLEASE HELP!!! MY BRAIN HURTS ME!!!

A possible solution maybe do y1(x)=y(x) , y2(x)=y'(x) and the problem is now

 

Y'=T(Y), T: R^2-> R^2 (obviously nonlinear)

 

then use the euler method

 

Yn+1=Yn+T(Yn)·DX

 

Other way... but I don't believe that it work in thisproblem is use

Raleigh-Ritz but I have use that method in problems

 

y''+f(x)y'+g(x)=0

 

that isn't the case...

 

Other way is read about Galerkin method but that is more related to PDE.