Solving this equation with Laplace transform?

Question

Can this equation be solved or at least put into a form of

$$F( L(u,t,s), L(u,x,s), L(u,y,s))=0$$

Using Laplace Transforms?

The equation: ${u}_{t}={u}_{x} + {u}_{y}~cos(y)$

B.Cs:

$u(x,y,0)=0$

$u(x,0,t)=f(x,t)$

$u(0,y,t)=g(y,t)$