1) Find all equilibrium solutions of the equation x = (1 − x) (x² − 4) and classify each one in terms of stability. Draw a phase space diagram and sketch by hand several typical solution curves. Describe the long term (t→∞) behavior of the solutions.

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 12CR
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please help me; im especially confsued on how to describe the long term behavior as t approaches positive and negative infinity 

1) Find all equilibrium solutions of the equation
x = (1-x)(x² - 4)
and classify each one in terms of stability. Draw a phase space diagram and sketch
by hand several typical solution curves. Describe the long term (t → ±∞) behavior
of the solutions.
Transcribed Image Text:1) Find all equilibrium solutions of the equation x = (1-x)(x² - 4) and classify each one in terms of stability. Draw a phase space diagram and sketch by hand several typical solution curves. Describe the long term (t → ±∞) behavior of the solutions.
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