Consider the following systems of rate of change equations:
System A:
$$\frac{dx}{dt}=3x(1-\frac{x}{10})-20xy$$ $$\frac{dy}{dt}=-5y+\frac{xy}{20}$$ System B: $$\frac{dx}{dt} = \frac{1}{3}x-\frac{xy}{100}$$ $$\frac{dy}{dt}=15y\left(1-\frac{y}{17}\right)+25xy$$ In one of these systems the prey are large animals and the predators are small animals. It takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey. Determine which system is which.
So I understand Lotka-Volterra models well enough, but this is not one of those apparently. There's a logistic equation-y look about it but I'm not sure what's going on. I tried using that $\frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{dy}{dt}$ to solve each system as an exact differential equation, but I can't find an integration factor that makes the partial derivatives equal in either case. How do I approach this?