Consider the differential equation dy dt = −y 4 + 8y 3 − 15y 2 . (1) a.find all equilibrium solutions of (1). b.draw the phase line of (1). c.draw representative solution curves of (1) in the t-y

Consider the differential equation dy dt = −y 4 + 8y 3 − 15y 2 . (1)

a.find all equilibrium solutions of (1).

b.draw the phase line of (1).

c.draw representative solution curves of (1) in the t-y plane.

d.classify each equilibrium solution as a source, sink, or node.

e.describe the behavior as t → ∞ of the solution of (1) corresponding to each given initial condition: i) y(0) = 100 ii) y(0) = 1 iii) y(0) = 0 iv) y(0) = −100