(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).

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Chapter2: Second-order Linear Odes
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Please help with D and E
(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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