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Consider the following system of differential equations à ý 2x - x² - y 1. The point (-2,-8), (0,0) and (1, 1) are equilibrium points for the system. Try to decide if they are locally asymptotically stable or saddle points. 2. Draw a phase diagram and indicate the above equilibrium points. For the quadrant * 20 and y ≥ 0 partition the phase diagram into regions with similar direction of motion. Indicate the direction of motion in each of the sectors by using arrows.

Consider the following system of differential equations à ý 2x - x² - y 1. The point (-2,-8), (0,0) and (1, 1) are equilibrium points for the system. Try to decide if they are locally asymptotically stable or saddle points. 2. Draw a phase diagram and indicate the above equilibrium points. For the quadrant * 20 and y ≥ 0 partition the phase diagram into regions with similar direction of motion. Indicate the direction of motion in each of the sectors by using arrows.

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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Task 4: Consider the following system of differential equations à = ý = 2x - x² - y 1. The point (-2,-8), (0,0) and (1,1) are equilibrium points for the system. Try to decide if they are locally asymptotically stable or saddle points. 2. Draw a phase diagram and indicate the above equilibrium points. For the quadrant 20 and y ≥ 0 partition the phase diagram into regions with similar direction of motion. Indicate the direction of motion in each of the sectors by using arrows.
Transcribed Image Text:Task 4: Consider the following system of differential equations à = ý = 2x - x² - y 1. The point (-2,-8), (0,0) and (1,1) are equilibrium points for the system. Try to decide if they are locally asymptotically stable or saddle points. 2. Draw a phase diagram and indicate the above equilibrium points. For the quadrant 20 and y ≥ 0 partition the phase diagram into regions with similar direction of motion. Indicate the direction of motion in each of the sectors by using arrows.
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