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Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear second-order differential equation x" + µ(x² − 1)x¹ + x = 0 where u is a real constant. (Assume y = x'.)

Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear second-order differential equation x" + µ(x² − 1)x¹ + x = 0 where u is a real constant. (Assume y = x'.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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Please also answer for u=0 and u=2

μ = -2 O stable node O unstable node O center stable spiral point unstable spiral point O degenerate stable node degenerate unstable node saddle point X
Transcribed Image Text:μ = -2 O stable node O unstable node O center stable spiral point unstable spiral point O degenerate stable node degenerate unstable node saddle point X
Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear second-order differential equation x" + μ(x² - 1)x' + x = 0 where u is a real constant. (Assume y = x'.)
Transcribed Image Text:Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear second-order differential equation x" + μ(x² - 1)x' + x = 0 where u is a real constant. (Assume y = x'.)
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