(Solved): 2. Consider the following two predator-prey systems of differential equations: (i) dtdx=10x(1 ...

2. Consider the following two predator-prey systems of differential equations: (i) $$\begin{array}{l}\frac{dx}{dt}=10x\left(1?\frac{x}{10}\right)?20xy\\ \frac{dy}{dt}=?5y+\frac{xy}{20}\end{array}$$ (ii) $$\begin{array}{l}\frac{dx}{dt}=0.3x?\frac{xy}{100}\\ \frac{dy}{dt}=15y\left(1?\frac{y}{15}\right)+25xy\end{array}$$ In one of these systems, the prey are very large animals and the predators are very small animals, such as elephants and mosquitos. Thus, 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, such as whales and krill. Determine which system is which and provide a justification for your answer.