PDEs, help with initial value Problem:

$$u_{tt}−u_{xx}+2u_{xy}−u_{yy}=0 \text{ with conditions }u(1,x,y)=\cos (x)+e^y$$
$$\text{and} u_t(1,x,y)=\sin (x)−y^2$$
I've gotten the solution to the point where I've solved for the general case and gotten:
$$u=ψ(x+t,y−t)+ϕ(x−t,y+t)$$
where phi and psi are arbitrary functions, but attempting to solve the initial conditions has resulted in nothing but problems, any help at all would be great.

Question

PDEs, help with initial value Problem:

$$u_{tt}−u_{xx}+2u_{xy}−u_{yy}=0 \text{ with conditions }u(1,x,y)=\cos (x)+e^y$$
$$\text{and} u_t(1,x,y)=\sin (x)−y^2$$
I've gotten the solution to the point where I've solved for the general case and gotten:
$$u=ψ(x+t,y−t)+ϕ(x−t,y+t)$$
where phi and psi are arbitrary functions, but attempting to solve the initial conditions has resulted in nothing but problems, any help at all would be great.