Consider the following autonomous first-order differential equation. O Find the critical points and phase portrait of the given differential equation. dx unstable y In(y + 2) asymptotically stable. semi-stable 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.) O DO 0 @O @ Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. @0 f (

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following autonomous first-order differential equation.
y In(y + 2)
Find the critical points and phase portrait of the given differential equation.
[I]
DO
O
unstable
0
Ⓡ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
semi-stable
O
0
✪
Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
1+++
3
Transcribed Image Text:Consider the following autonomous first-order differential equation. y In(y + 2) Find the critical points and phase portrait of the given differential equation. [I] DO O unstable 0 Ⓡ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 semi-stable O 0 ✪ Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. 1+++ 3
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