First, show that (0,0) is the only equilibrium of the differential equation (multiply x by x and y by y) d ■x(t) = 4x + 2y − x(x² + y²) d - dt³ (t) = −2x + y − y(x² + y²) Next, write the differential equation in polar co-ordinates [recall that x(t) = rcos(0).] Then, prove that there is at least one limit cycle

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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First, show that (0,0) is the only equilibrium of the differential equation (multiply x by x
and y by y)
d
■x(t) = 4x + 2y − x(x² + y²)
d
-
dt³ (t) = −2x + y − y(x² + y²)
Next, write the differential equation in polar co-ordinates [recall that x(t) = rcos(0).]
Then, prove that there is at least one limit cycle
Transcribed Image Text:First, show that (0,0) is the only equilibrium of the differential equation (multiply x by x and y by y) d ■x(t) = 4x + 2y − x(x² + y²) d - dt³ (t) = −2x + y − y(x² + y²) Next, write the differential equation in polar co-ordinates [recall that x(t) = rcos(0).] Then, prove that there is at least one limit cycle
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