Classify the critical points 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 y=0 unstable semi-stable None

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the autonomous DE ay/dx = (2/2)y – sin y. Determine the critical points of
the equation. Discuss a way of obtaining a phase portrait of the equation.
(Enter your answers using interval notation.)
Since
(2/x)y – sin y > 0 for
YE
and
(2/x)y – sin y < 0
for
y E
one obtains the following phase portrait.
Classify the critical points 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
y=0
unstable
semi-stable
None
EIN
EIN
Transcribed Image Text:Consider the autonomous DE ay/dx = (2/2)y – sin y. Determine the critical points of the equation. Discuss a way of obtaining a phase portrait of the equation. (Enter your answers using interval notation.) Since (2/x)y – sin y > 0 for YE and (2/x)y – sin y < 0 for y E one obtains the following phase portrait. Classify the critical points 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 y=0 unstable semi-stable None EIN EIN
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