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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb63c1825-1a47-49b5-b570-42b0f113327a%2F519033f0-d73d-4135-9439-f6d67f0c98d2%2Fsva49k_processed.jpeg&w=3840&q=75)
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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