What's the condition for
$\dot{x} = f(x,y)\\ \dot{y} = g(x,y)$
To be rewritable as
$\dot{x} = \frac{\partial F(x,y)}{\partial y}\\ \dot{y} = -\frac{\partial F(x,y)}{\partial x}$
Can I always find a transformation $z=z(x,y)$ such that
$\dot{x} = \frac{\partial G(x,y)}{\partial z}\\ \dot{z} = -\frac{\partial G(x,y)}{\partial x}$
