Consider the following autonomous first-order differential equation. dy = dx = y² - 4y Find the critical points and phase portrait of the given differential equation. 4 4 0 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4-3

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.)
asymptotically stable
unstable
semi-stable
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
y
-4
X
-4
@
y
@O
-4
y
X
Transcribed Image Text: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.) asymptotically stable unstable semi-stable Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y y -4 X -4 @ y @O -4 y X
Consider the following autonomous first-order differential equation.
dy =
dx
= y² - 4y
Find the critical points and phase portrait of the given differential equation.
0
0
ܠܚ
0
-4
Transcribed Image Text:Consider the following autonomous first-order differential equation. dy = dx = y² - 4y Find the critical points and phase portrait of the given differential equation. 0 0 ܠܚ 0 -4
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