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).

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Related Book For  book-img-for-question

Mathematics And Statistics For Science

ISBN: 9783031053177

1st Edition

Authors: James Sneyd, Rachel M. Fewster, Duncan McGillivray

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