问题

例.  设二元隐函数 $u=u(x,y)$, $v=v(x,y)$ 由方程组

\[
\begin{cases}
2x=v^2-u^2,\\
y=uv,
\end{cases}
\]

确定, 求 $\dfrac{\partial u}{\partial x}$, $\dfrac{\partial u}{\partial y}$, $\dfrac{\partial v}{\partial x}$, $\dfrac{\partial v}{\partial y}$.