Equations 7.63 and 7.64 are solved using the assumed solutions \(y(x, t)=Y(x) \exp (i \omega t)\) and \(\psi(x, t)=\Psi(x) \exp (i \omega t)\). Find the characteristic equation.

a [GA(2) x 2 -m(x). +p(x,t) = 0 (7.63) t 3 (EI (x) 3x)- + GA(x) (x-4) -k(x)m(x)- 0. (7.64) t