Given that a system is a gradient system, here's how to find it's potential function V. Suppose that $\displaystyle x'=f(x,y)$ and $\displaystyle y'=g(x,y).$ Then $\displaystyle x'=-\nabla V$ implies $\displaystyle f(x,y)=-\frac{\partial V}{\partial x}$ and $\displaystyle g(x,y)=-\frac{\partial V}{\partial y}$.

Use this procedure to find V for the following gradient system:

$\displaystyle x'=y^2+y cos x$

$\displaystyle y'=2xy+sin x$