Nonlinear Systems & Linearization · Medium problem

For the predator–prey system $x' = x(2 - y),\; y' = y(x - 3)$ with $x, y > 0$, there are constants $a$ and $b$ for which $V(x, y) = x - a\ln x + y - b\ln y$ is constant along every trajectory. With those constants, find the minimum value of $V$ over all $x, y > 0$.