Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 3.2, Problem 22E
Doomsday or extinction Suppose the population model (4) is modified to be
dPdt=P(bP−a).
- (a) If a > 0, b > 0 show by means of a phase portrait (see page 40) that, depending on the initial condition P(0) = P0, the mathematical model could include a doomsday scenario (P(t) → ∞) or an extinction scenario (P(t) → 0).
- (b) Solve the initial-value problem
dPdt=P(0.0005P−0.1),P(0)=300.
Show that this model predicts a doomsday for the population in a finite time T.
- (c) Solve the differential equation in part (b) subject to the initial condition P(0) = 100. Show that this model predicts extinction for the population as t → ∞.
dPdt=P(a−bP).
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Chapter 3 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
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