SHM ODE Problem: Finding Y General

[mistereko]

Homework Statement

I've got

y'' - ω²y = sin(ωx) + sinh(ωx) where y(a) = A, y(b) = B

Homework Equations

The Attempt at a Solution

Y_c = C₁ Sinh(ωx) + C₂ Cosh(ωx)

and I got my Y_p to be -1/2*sin(ωx) + 1/2*sinh(ωx)

I'm not sure about getting the Y general. Any pointers?

Thanks

 

[HallsofIvy]

The whole point of finding "Y_c" and "Y_p" is that the general solution to the entire equation is the sum of those.