Consider the logistic differential equation, with harvesting dP = 0.08P (1 - 15 1000 dt where P(t) represents a fish population at time t, measured in weeks. (a) Find the equilibrium solutions and determine their nature. (b) Draw the phase diagram for the differential equation. (c) Sketch several solution curves. Describe what happens to the fish population for various initial populations.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the logistic differential equation, with harvesting
*- 0sr (1-) - 15
dP
dt
P
0.08P
1000
where P(t) represents a fish population at time t, measured in weeks.
(a) Find the equilibrium solutions and determine their nature.
(b) Draw the phase diagram for the differential equation.
(c) Sketch several solution curves. Describe what happens to the fish population for various
initial populations.
(d) Solve the differential equation explicitly, with initial populations Po = 200, and Po = 300.
%3!
Transcribed Image Text:Consider the logistic differential equation, with harvesting *- 0sr (1-) - 15 dP dt P 0.08P 1000 where P(t) represents a fish population at time t, measured in weeks. (a) Find the equilibrium solutions and determine their nature. (b) Draw the phase diagram for the differential equation. (c) Sketch several solution curves. Describe what happens to the fish population for various initial populations. (d) Solve the differential equation explicitly, with initial populations Po = 200, and Po = 300. %3!
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