I have been asked to derive a solution for F(y) in the form F(y) = A cos ky + B sin ky + C , where k = (1 + I)/δ , δ = sqrt(2ν/ω) and A,B and C are constants to be found.
The ODE I have found is F''+(iω/ν)F+a/ν = 0 with the boundary conditions f(h/2)=f(-h/2) = 0, where a and ω are real constants.
My question is, what are the steps i need to take to solve this ode? and furthermore is my ODE in the correct form such that i will derive a solution for F(y)in the form asked above?