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7. Show that the system L' = 3y + 2x – r(4x² + 2y²), / = -3r + 2y – y(4.x² + 2y?), has at least one closed path on the annulus 1/2 < r² + y? < 1. You may assume that the origin is the only equilibrium point.

7. Show that the system L' = 3y + 2x – r(4x² + 2y²), / = -3r + 2y – y(4.x² + 2y?), has at least one closed path on the annulus 1/2 < r² + y? < 1. You may assume that the origin is the only equilibrium point.

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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7. Show that the system a' = 3y + 2x – x(4.x2 + 2y?), y = -3.r + 2y – y(4.x2 + 2y?), has at least one closed path on the annulus 1/2 < x? + y? < 1. You may assume that the origin is the only equilibrium point. Hint: Consider the scalar product of the tangent f = [a' y']" and outward normal n = [x y]" to the circle r + y? = R2. %3D
Transcribed Image Text:7. Show that the system a' = 3y + 2x – x(4.x2 + 2y?), y = -3.r + 2y – y(4.x2 + 2y?), has at least one closed path on the annulus 1/2 < x? + y? < 1. You may assume that the origin is the only equilibrium point. Hint: Consider the scalar product of the tangent f = [a' y']" and outward normal n = [x y]" to the circle r + y? = R2. %3D
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