Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y 4 6 -6 -4 -2 2 -6 -4 -2 -2 -2 2 2 4 6 x 2
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y 4 6 -6 -4 -2 2 -6 -4 -2 -2 -2 2 2 4 6 x 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
X
4
-2
4
-6
-4
-2
2
O
-4
-2
y
2
2
4
6
6
x
O
-6
-4
-2
y
6
2
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd559a6b-d72a-4e29-9f26-669521aaff57%2F28dc575a-6ef6-4f86-871a-d71b26d72eb0%2Fwtbafph_processed.png&w=3840&q=75)
Transcribed Image Text:Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
X
4
-2
4
-6
-4
-2
2
O
-4
-2
y
2
2
4
6
6
x
O
-6
-4
-2
y
6
2
X
![Consider the following autonomous first-order differential equation.
dy = y²(9- y²)
dx
Find the critical points and phase portrait of the given differential equation.
6
3
3
0
0
0
0
-6
-6
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd559a6b-d72a-4e29-9f26-669521aaff57%2F28dc575a-6ef6-4f86-871a-d71b26d72eb0%2Fbsaunuq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following autonomous first-order differential equation.
dy = y²(9- y²)
dx
Find the critical points and phase portrait of the given differential equation.
6
3
3
0
0
0
0
-6
-6
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
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