For a system I am studying, I know that the Jacobian for a transformation from variables $u(x,y)$ and $v(x,y)$ to $x$ and $y$ must be equal to a function $p(x,y)$ which is known. I want to find what $u(x,y)$ and $v(x,y)$ are in terms of $p(x,y)$. The equation to solve is:
$$ p(x,y) = \frac{\partial u}{\partial x}\frac{\partial v}{\partial y} - \frac{\partial u}{\partial y}\frac{\partial v}{\partial x}$$
where $p(x,y)$ is a known function and $u$ and $v$ depend on both $x$ and $y$. Any advice?