Consider a differential equation du dt = p(u), where p(u) has the graph shown in Fig. 25.13.
Question:
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).
Step by Step Answer:
Related Book For
Mathematics And Statistics For Science
ISBN: 9783031053177
1st Edition
Authors: James Sneyd, Rachel M. Fewster, Duncan McGillivray
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