Consider the following autonomous first-order differential equation. dy = y²(4- y²) da (a) Which of the following is the phase portrait for the differential equation? -2 A B (b) List the critical points and classify each critical point as asymptotically stable, unstable, or semistable. (c) Sketch the actual solutions in the - y plane. Make sure to sketch the equilibrium solutions. Make sure you sketch typical solution curves in all the regions in the r-y. Make sure to label your graph. 4 4 6 -2 2 0 -0 2
Consider the following autonomous first-order differential equation. dy = y²(4- y²) da (a) Which of the following is the phase portrait for the differential equation? -2 A B (b) List the critical points and classify each critical point as asymptotically stable, unstable, or semistable. (c) Sketch the actual solutions in the - y plane. Make sure to sketch the equilibrium solutions. Make sure you sketch typical solution curves in all the regions in the r-y. Make sure to label your graph. 4 4 6 -2 2 0 -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
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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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