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 10 0 0 -10 O O O 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 Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. 10 -6 O -6 0 -10 -4 -2 5 0

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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Consider the following autonomous first-order differential equation.

dy
dx
 = y2(25 − y2)

Find the critical points and phase portrait of the given differential equation.

       


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    
 
 
 


Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.

Consider the following autonomous first-order differential equation.
dx=y²(25 - y²)
Find the critical points and phase portrait of the given differential equation.
10
10
5
5
0
0
0
0
-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
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
10
-2
2
O
-6
-4
-4
-2
-2
-10-
2
2
O
-2
10
-10
Transcribed Image Text:Consider the following autonomous first-order differential equation. dx=y²(25 - y²) Find the critical points and phase portrait of the given differential equation. 10 10 5 5 0 0 0 0 -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 Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. 10 -2 2 O -6 -4 -4 -2 -2 -10- 2 2 O -2 10 -10
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