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(d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq. (3). (iii) stability of the critical points by drawing a phase diagram for Eq. (3).

(d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq. (3). (iii) stability of the critical points by drawing a phase diagram for Eq. (3).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq. (3). (iii) stability of the critical points by drawing a phase diagram for Eq. (3). (e) (i) Taking y(0) = 11 and a step size of h = 1/12, apply four iterations of the Forward Euler Formula to approximate the solution of Eq. (3). Apply two decimal place rounding where applicable. (ii) How do your results from (e) (i) compare with what the phase diagram for Eq. (3) reveals?
Transcribed Image Text:(d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq. (3). (iii) stability of the critical points by drawing a phase diagram for Eq. (3). (e) (i) Taking y(0) = 11 and a step size of h = 1/12, apply four iterations of the Forward Euler Formula to approximate the solution of Eq. (3). Apply two decimal place rounding where applicable. (ii) How do your results from (e) (i) compare with what the phase diagram for Eq. (3) reveals?
Suppose that the differential equation dy dt = y(40-y) - 300 models a logistic equation with harvesting, where y(t) represents a spotted grunter popu- lation (Figure 1) in the Knysna Lagoon at time t, measured in years. ⒸSAIAB Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/)
Transcribed Image Text:Suppose that the differential equation dy dt = y(40-y) - 300 models a logistic equation with harvesting, where y(t) represents a spotted grunter popu- lation (Figure 1) in the Knysna Lagoon at time t, measured in years. ⒸSAIAB Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/)
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