设函数 $f(u, v)$ 具有二阶连续偏导数，且 $\frac{\partial^2 f}{\partial u^2}+\frac{\partial^2 f}{\partial v^2}=3$ ，令 $z=f\left(x y, \frac{x^2-y^2}{2}\right)$ ，求 $\left.\left(\frac{\partial^2 z}{\partial x^2}+\frac{\partial^2 z}{\partial y^2}\right)\right|_{x=2, y=3}$.