Consider the following autonomous first-order differential equation. dy = y In(y + 2) Find the critical points and phase portrait of the given differential equation. 0 unstable Ⓡ semi-stable O 0 Ⓡ NONE 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 -1 0 o Ⓡ Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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10.
DETAILS
ZILLDIFFEQMODAP11 2.1.027.
Consider the following autonomous first-order differential equation.
= y In(y + 2)
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 -1
unstable
semi-stable
0
0
NONE
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
Transcribed Image Text:10. DETAILS ZILLDIFFEQMODAP11 2.1.027. Consider the following autonomous first-order differential equation. = y In(y + 2) 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 -1 unstable semi-stable 0 0 NONE Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
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