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1. Consider the differential equation y = y³-3y² + 2y. (a) Find all equilibrium solutions and determine whether they are asymptotically stable or unstable. (Verify your answer.) (b) Sketch the graphs of the solutions satisfying the initial conditions y(0) = 0.1. y(0) = 0.9, y(0) = 1.1 and y(0) = 1.9. (Show the inflection point and concavity of the solution curve.)

1. Consider the differential equation y = y³-3y² + 2y. (a) Find all equilibrium solutions and determine whether they are asymptotically stable or unstable. (Verify your answer.) (b) Sketch the graphs of the solutions satisfying the initial conditions y(0) = 0.1. y(0) = 0.9, y(0) = 1.1 and y(0) = 1.9. (Show the inflection point and concavity of the solution curve.)

Advanced Engineering Mathematics
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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1. Consider the differential equation y = y³ - 3y² + 2y. (a) Find all equilibrium solutions and determine whether they are asymptotically stable or unstable. (Verify your answer.) (b) Sketch the graphs of the solutions satisfying the initial conditions y(0) = 0.1. y(0) = 0.9. y(0) = 1.1 and y(0) = 1.9. (Show the inflection point and concavity of the solution curve.)
Transcribed Image Text:1. Consider the differential equation y = y³ - 3y² + 2y. (a) Find all equilibrium solutions and determine whether they are asymptotically stable or unstable. (Verify your answer.) (b) Sketch the graphs of the solutions satisfying the initial conditions y(0) = 0.1. y(0) = 0.9. y(0) = 1.1 and y(0) = 1.9. (Show the inflection point and concavity of the solution curve.)
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