Well, y=x is an obvious solution, but for a more general one (or less trivial) I really don't know how to attack this. To give you an idea you could try this
-sin(y) + sin(x) = y''
(of course y=y(x) and y'' means (d^2y)/(dx^2) )
I'm looking for solution (elliptical integral maybe?), or at least an advice how to solve this.
The numerical solution (runge kutta or something) with Mathematica or Mathlab will also be very good.
I just have no idea how to solve this, and if anyone has done something similar, please advice!!!