What type of differential equation


New member
Feb 28, 2019
A population r(t) of rabbits (at time t) satisfies
dr/dt = kr (1 − r/r∗) − αfr
where k > 0 is a constant representing the rabbit breeding rate, r∗ > 0 is the (constant) maximum sustainable rabbit population size in the absence of predation, f > 0 is the population of foxes, and α > 0 is the (constant) rate of predation of rabbits by foxes.
Suppose that the fox population, f, is constant. Solve the differential equation above, and determine
(a) the size of the rabbit population as t → ∞;
(b) the maximum predation rate α for which the rabbit population does not die out as t → ∞;
(c) the value of α which maximises αfr (the total number of rabbits caught) as t → ∞, and the corresponding rabbit population.

Subhotosh Khan

Super Moderator
Staff member
Jun 18, 2007
How many types of differential equations you know of? What are those? We need to know this - ao that we know where to begin to help you.