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Consider the differential equation = y(y - 3)² - 00<% <∞⁰ Find all equilibrium solutions. " Draw the phase line and then draw at least one solution curve between each equilibrium solution. Classify each equilibrium solution as stable, unstable or semi-stable. Based on the phase portrait, determine the behavior of y as t → ∞ If this behavior depends on the initial value of y at t = 0, describe this dependency.

Consider the differential equation = y(y - 3)² - 00<% <∞⁰ Find all equilibrium solutions. " Draw the phase line and then draw at least one solution curve between each equilibrium solution. Classify each equilibrium solution as stable, unstable or semi-stable. Based on the phase portrait, determine the behavior of y as t → ∞ If this behavior depends on the initial value of y at t = 0, describe this dependency.

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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Consider the differential equation = y(y - 3)² dt Find all equilibrium solutions. } -∞0 <yo <∞ Draw the phase line and then draw at least one solution curve between each equilibrium solution. Classify each equilibrium solution as stable, unstable or semi-stable. Based on the phase portrait, determine the behavior of y as t → ∞0 If this behavior depends on the initial value of y at t = 0, describe this dependency.
Transcribed Image Text:Consider the differential equation = y(y - 3)² dt Find all equilibrium solutions. } -∞0 <yo <∞ Draw the phase line and then draw at least one solution curve between each equilibrium solution. Classify each equilibrium solution as stable, unstable or semi-stable. Based on the phase portrait, determine the behavior of y as t → ∞0 If this behavior depends on the initial value of y at t = 0, describe this dependency.
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