Consider the following autonomous first-order differential equation. dy - y?(25 - y?) Find the critical points and phase portrait of the given differential equation. 10 10 -10 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 c asymptotically stable unstable 00

Calculus: Early Transcendentals
8th Edition
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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Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
y
10-
X
X
-6
-4
-2
2
4.
-2
4
-10-
10
X
4
-2
2
4
6.
-4
-2
-10-
Transcribed Image Text:Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. y 10- X X -6 -4 -2 2 4. -2 4 -10- 10 X 4 -2 2 4 6. -4 -2 -10-
Consider the following autonomous first-order differential equation.
dy
= y²(25 – y²)
dx
Find the critical points and phase portrait of the given differential equation.
10
5
10
-10
-10
-5
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
Transcribed Image Text:Consider the following autonomous first-order differential equation. dy = y²(25 – y²) dx Find the critical points and phase portrait of the given differential equation. 10 5 10 -10 -10 -5 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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