5. Consider the following autonomous first-order differential equation. dy da = y²(4- y²) (a) Which of the following is the phase portrait for the differential equation? 2 0 0 A B с D (b) List the critical points and classify each critical point as asymptotically stable, unstable, or semistable. (c) Sketch the actual solutions in the zy plane. Make sure to sketch the equilibrium solutions. Make sure you sketch typical solution curves in all the regions in the 2- y. Make sure to label your graph. Y 4 6 82 2 2 0 2
5. Consider the following autonomous first-order differential equation. dy da = y²(4- y²) (a) Which of the following is the phase portrait for the differential equation? 2 0 0 A B с D (b) List the critical points and classify each critical point as asymptotically stable, unstable, or semistable. (c) Sketch the actual solutions in the zy plane. Make sure to sketch the equilibrium solutions. Make sure you sketch typical solution curves in all the regions in the 2- y. Make sure to label your graph. Y 4 6 82 2 2 0 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
![5.
Consider the following autonomous first-order differential equation.
dy
da
= y²(4- y²)
(a) Which of the following is the phase portrait for the differential equation?
0
-2
B
(b) List the critical points and classify each critical point as asymptotically stable, unstable, or
semistable.
(c) Sketch the actual solutions in the r- y plane. Make sure to sketch the equilibrium solutions.
Make sure you sketch typical solution curves in all the regions in the a-y. Make sure to label
your graph.
Y
4
6
-2
4
2
0
-0
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feaa11b37-8537-405e-bace-456af8709c1e%2F1b679596-852d-4706-915c-056efdfa97dd%2Fu97djsw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.
Consider the following autonomous first-order differential equation.
dy
da
= y²(4- y²)
(a) Which of the following is the phase portrait for the differential equation?
0
-2
B
(b) List the critical points and classify each critical point as asymptotically stable, unstable, or
semistable.
(c) Sketch the actual solutions in the r- y plane. Make sure to sketch the equilibrium solutions.
Make sure you sketch typical solution curves in all the regions in the a-y. Make sure to label
your graph.
Y
4
6
-2
4
2
0
-0
2
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