I'm trying to come up with other examples of $F_1$, $F_2$ such that: $$\frac{\partial F_1}{\partial x} - \frac{\partial F_2}{\partial y} = 1$$
I know the standard $F(x,y) = (-\frac{y}{2}, \frac{x}{2})$ works, but I'm wondering if there are other vector fields satisfying this?