Problem 3 For the autonomous equation y' = y³ + y² - 6y,(1) Find its equilibrium solutions.(2) For each equilibrium solution, determine its stability. Justify your answer.(3) If y(0) = -3, what is lim y(x)?

Introduction: An autonomous equation is a type of differential equation where the independent…

Answered: Problem 3 For the autonomous equation…

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.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

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Problem 3 For the autonomous equation y' = y³ + y² - by, (1) Find its equilibrium solutions. (2) For each equilibrium solution, determine its stability. Justify your answer. (3) If y(0) = -3, what is lim y(x)? ΣΕ 100