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Exam style question 1. Show that both (0,0) and (1,0) are both equilibria of the ODE d dt x(t)=x+xy−(x+y) (x² + y²) 1/2 d dt πy (t) = y − x² + (x − y) (x² + y²)1/2 2. Linearise the system at both of these equilibria points. What can you conclude regarding stability of each equilibrium point? 3. Convert the system to polar co-ordinates (r(t),0(t)).

Exam style question 1. Show that both (0,0) and (1,0) are both equilibria of the ODE d dt x(t)=x+xy−(x+y) (x² + y²) 1/2 d dt πy (t) = y − x² + (x − y) (x² + y²)1/2 2. Linearise the system at both of these equilibria points. What can you conclude regarding stability of each equilibrium point? 3. Convert the system to polar co-ordinates (r(t),0(t)).

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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Exam style question 1. Show that both (0,0) and (1,0) are both equilibria of the ODE d dt x(t)=x+xy−(x+y) (x² + y²) 1/2 d dt πy (t) = y − x² + (x − y) (x² + y²)1/2 2. Linearise the system at both of these equilibria points. What can you conclude regarding stability of each equilibrium point? 3. Convert the system to polar co-ordinates (r(t),0(t)).
Transcribed Image Text:Exam style question 1. Show that both (0,0) and (1,0) are both equilibria of the ODE d dt x(t)=x+xy−(x+y) (x² + y²) 1/2 d dt πy (t) = y − x² + (x − y) (x² + y²)1/2 2. Linearise the system at both of these equilibria points. What can you conclude regarding stability of each equilibrium point? 3. Convert the system to polar co-ordinates (r(t),0(t)).
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