5. Recall that a 1* order, autonomous equation can be written in general as = f(y). Consider the equation: - y3 – y? – 2y dr (a) Find the equilibrium solutions (critical points) of the equation. (b) Draw a phase diagram of y vs. f(y) (make sure to label the sketch). (c) Sketch of the actual solutions of r vs. y (make sure to label the sketch). (d) Characterize the stability of the equilibrium solutions (e.g. stable, unstable, semi-stable).
5. Recall that a 1* order, autonomous equation can be written in general as = f(y). Consider the equation: - y3 – y? – 2y dr (a) Find the equilibrium solutions (critical points) of the equation. (b) Draw a phase diagram of y vs. f(y) (make sure to label the sketch). (c) Sketch of the actual solutions of r vs. y (make sure to label the sketch). (d) Characterize the stability of the equilibrium solutions (e.g. stable, unstable, semi-stable).
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. Recall that a 1st order, autonomous equation can be written in general as 4 = f(y). Consider
the equation:
dy
dr
y3 – y² – 2y
(a) Find the equilibrium solutions (critical points) of the equation.
(b) Draw a
gram of y vs. f(y) (make sure to label the
ch).
ase
(c) Sketch of the actual solutions of æ vs. y (make sure to label the sketch).
(d) Characterize the stability of the equilibrium solutions (e.g. stable, unstable, semi-stable).
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