I can't seem to figure this one out
Two guerilla forces, with troop strength $x(t)$ and $y(t)$, are in combat with each other without reinforcement. Suppose the territory is rather large and full of places to hide. The $y$-force needs to find the $x$-force first before it can inflict combat losses, and the higher the $x$, the easier it is for them to be found. Therefore, the combat loss rate for the $x$-force should be proportional $x$ . $y$ (this is unlike conventional warfare, where the full force of $x$ is open to be shot at by $y$, and so the combat loss rate for $x$ shouldn't depend on the total number of the $x$-force). Thus $\frac{dx}{dt} = -axy$ and $\frac{dy}{dt} = -bxy$
where $a$ is the combat effectiveness of the $y$-force and $b$ is that of the $x$-force. Suppose initially that $x_0$ and $y_0$ are the troop strengths for the $x$- and $y$-forces, and that $x_0$ is three times as numerous as $y_0$. How much more effective must the $y$-force be to stalemate it's enemy?