Consider a differential equation du dt

= p(u), where p(u) has the graph shown in Fig. 25.13.

a. At what values of u does this differential equation have equilibrium points?

b. Sketch the phase line for this differential equation.

c. For each interval bounded by equilibrium points, describe the long-term behaviour of solutions which start in this interval. Make sure you consider the cases t → ∞ and t → −∞.

d. Thus, describe the long-term behaviour of solutions of the differential equation dk db = 100(k − 1)(k − 0.5)k 2 (k + 0.5).