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*() find the critical points stating the stability of each of these points (H) sketch the phase portrait and the phase plane diagram

*() find the critical points stating the stability of each of these points (H) sketch the phase portrait and the phase plane diagram

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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Solve b part and also subparts of b only in two hours if u can't solve this u can reject in one hour so that i can't wait of your answer plz..
o) The population of fish in a loch grows naturally according to a logistic model. An average of 1000 fish per year are removed, leading to the population equation: dr = 7x - x? - 10 where x is the fish population in hundreds at time t. What could each of the elements of the differential equation relate to? *() find the critical points stating the stability of each of these points • (i) sketch the phase portrait and the phase plane diagram Describe in words the long-term outcome for the population if initially there are: (ii) 1800 fish (iv) 400 fish (v) 300 fish (vi) 150 fish
Transcribed Image Text:o) The population of fish in a loch grows naturally according to a logistic model. An average of 1000 fish per year are removed, leading to the population equation: dr = 7x - x? - 10 where x is the fish population in hundreds at time t. What could each of the elements of the differential equation relate to? *() find the critical points stating the stability of each of these points • (i) sketch the phase portrait and the phase plane diagram Describe in words the long-term outcome for the population if initially there are: (ii) 1800 fish (iv) 400 fish (v) 300 fish (vi) 150 fish
Question 2 (a) Consider the following autonomous first order differential equation:- dx dt = x(x – 4)(x – 2) i) Find the critical points and hence state the equilibrium solutions and determine the stability of each critical point. ii) Sketch the phase portrait and the phase plane diagram.
Transcribed Image Text:Question 2 (a) Consider the following autonomous first order differential equation:- dx dt = x(x – 4)(x – 2) i) Find the critical points and hence state the equilibrium solutions and determine the stability of each critical point. ii) Sketch the phase portrait and the phase plane diagram.
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