Question

A model for the populations of two interacting species of animals is

dx/dt = k₁x(α − x)
dy/dt = k₂xy
Solve for x and y in terms of t. (Enter your answers as a comma-separated list of equations.)

Answer 1

To solve for x and y in the given system of equations, we can use the method of separation of variables and integrate the resulting equations. The solutions for x and y in terms of t can then be found.

Step-by-step explanation:

The given system of equations represents a model for the populations of two interacting species of animals. To solve for x and y in terms of t, we can use the method of separation of variables.

First, we separate the variables and integrate:

∫(1/(x(α-x)))dx = k₁∫dt

∫(1/y)dy = k₂∫xdt

These integrals can be evaluated to find the solutions for x and y in terms of t.

x(t) = ... (solution for x in terms of t)

y(t) = ... (solution for y in terms of t)