Consider the following autonomous first-order differential equation. =y² - 2y dx Find the critical points and phase portrait of the given differential equation. 2 0 unstable asymptotically stable 0 semi-stable e 0 Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there NONE.) -2 2

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following autonomous first-order differential equation.
dy
:y² - 2y
dx
Find the critical points and phase portrait of the given differential equation.
2
0
unstable
0
III
-2
-2
asymptotically stable
Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there are no critical points in a certain category, enter
NONE.)
semi-stable
2
0
Transcribed Image Text:Consider the following autonomous first-order differential equation. dy :y² - 2y dx Find the critical points and phase portrait of the given differential equation. 2 0 unstable 0 III -2 -2 asymptotically stable Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there are no critical points in a certain category, enter NONE.) semi-stable 2 0
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
y
-2
-2
4
2
y
2
X
- x
2
-2
2
+ X
2
-2
y
2
+ X
2
Transcribed Image Text:Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y y -2 -2 4 2 y 2 X - x 2 -2 2 + X 2 -2 y 2 + X 2
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