$2$ Consider an unsteady viscous liquid flowing between two parallel plates as shown. The plates are stationary. The equation of motion of fluid velocity $u(y,t)$ is given as

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}=v\frac{de{l}^{2}u}{del{y}^2}+siny$

Assuming unsteady fully developed flow starting from rest, evaluate the velocity $u(y,t).$