Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
-6
4
-4
-2
-2
y
2
2
4
6
X
-6
-4
-4
-2
-2
y
2
4
6
X
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Transcribed Image Text:Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y -6 4 -4 -2 -2 y 2 2 4 6 X -6 -4 -4 -2 -2 y 2 4 6 X
Consider the following autonomous first-order differential equation.
dy = y²(16 - y²)
dx
Find the critical points and phase portrait of the given differential equation.
-8
asymptotically stable 4
unstable.
semi-stable
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 are no critical points in a certain category, enter
NONE.)
none
X
4
X
0
X
8
0
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Transcribed Image Text:Consider the following autonomous first-order differential equation. dy = y²(16 - y²) dx Find the critical points and phase portrait of the given differential equation. -8 asymptotically stable 4 unstable. semi-stable 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 are no critical points in a certain category, enter NONE.) none X 4 X 0 X 8 0
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