Solve the problem.
-The system of equations $\frac { d x } { d t } = ( - 2 + 3 y ) x$ and $\frac { d y } { d t } = ( - 2 + x ) y$ describes the growth rates of two symbiotic (dependent) species of animals (such as the rhinoceros and a type of bird which eats insects from its back). What is necessarily true of the two populations at the equilibrium points?
A) They are both at a maximum.
B) Both populations equal zero.
C) They are both at a minimum.
D) They both remain constant over all time.

Question

Quizplus · Accepted Answer

At equilibrium points, the growth rates of both populations are zero, meaning $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} = 0$, which implies that the populations are not changing, hence they remain constant over time.

Solve the Problem dxdt=(−2+3y)x\frac { d x } { d t } = ( - 2 + 3 y ) xdtdx​=(−2+3y)x

Solve the Problem $\frac { d x } { d t } = ( - 2 + 3 y ) x$