When two species, such as the rhinoceros and birds pictured below, coexist in a symbiotic (dependent) relationship, they either increase together or decrease together. Typical equations for the growth rates of two such species might be

(a) Find an equation relating x and y if x = 5 when y = 1.
(b) Find values of x and y so that both populations are constant.
(c) A graph of the relationship found in part (a) is shown in the figure. Based on the differential equations for the growth rate and this graph, what happens to both populations when y > 1? When y < 1?

Transcribed Image Text:

dx dt dy dt = -4x + 4xy = -3y + 2xy.