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Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (1 + In(x) + x) dx dx = (7-In(x)) dy

Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (1 + In(x) + x) dx dx = (7-In(x)) dy

Advanced Engineering Mathematics
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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Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (₁ 1 + In(x) + +2) ₁ dx = (7-In(x)) dy
Transcribed Image Text:Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (₁ 1 + In(x) + +2) ₁ dx = (7-In(x)) dy
Consider the following autonomous first-order differential equation. = y In(y + 2) dx Find the critical points and phase portrait of the given differential equation. 0 0 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
Transcribed Image Text:Consider the following autonomous first-order differential equation. = y In(y + 2) dx Find the critical points and phase portrait of the given differential equation. 0 0 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
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