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
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
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2F68ea42cb-0bf7-492c-8c12-9c01a35458bd%2Fjeva1b_processed.png&w=3840&q=75)
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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