The equations of Lotka and Volterra* Where are positive constants, occur in t...

The equations of Lotka and Volterra*

Where are positive constants, occur in the analysis of the biological balance of two species of animals such as predators and prey (for example, foxes and rabbits). Here x(t) and y(t) denote the populations of the two species at time t. Although no explicit solutions of the system exist, solutions can be found relating the two populations at any time. Divide the first equation by the second and solve the resulting non-linear first-order differential equation.