Problem 5 of the problems in 4.1 and 4.2 asks to "Consiser oscillations of the beam with the clamped left and the free right end. The boundary conditions are then $$u_{to}+Ku_{xxxx}=0, 0<x<l (9)$$and $$u_{xx}(l,t)=u_{xxx}(l,t)=0 (13)$$. After separating variables and pluggin in boundary counditikns, I get
$$-A \sin(\omega L)-B \cos(\omega L)+ C \sinh(\omega L)+D \cosh(\omega L)=0$$ and
$$A\cos(\omega L)+B \sin(\omega L)+C \cosh(\omega L)+ D \sinh(\omega L)=0$$
This is two equations and four unknowns. How can I solve for A, B, C, D?
