Find the complete integral of partial differential equation
$$\displaystyle z^2 = pqxy $$
I have solved this equation till auxiliary equation:
$$\displaystyle \frac{dp}{-pqy+2pz}=\frac{dq}{-pqx+2qz}=\frac{dz}{2pqxy}=\frac{dx}{qxy}=\frac{dy}{pxy} $$
But I have unable to find value of p and q.
EDIT:
p = ∂z/∂x
q = ∂z/∂y
r = ∂²z/∂x² = ∂p/∂x
s = ∂²z/∂x∂y = ∂p/∂y or ∂q/∂x
t = ∂²z/∂y² = ∂q/∂y