Find the critical points and phase portrait of the given autonomous first-order differential equation. Classify each critical
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Find the critical points and phase portrait of the given autonomous first-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.
1. dy/dx = y2 – 3y
2. dy/dx = y2 – y3
3. dy/dx = (y - 2)4
4. dy/dx = 10 + 3y – y2
5. dy/dx = y2(4 – y2)
6. dy/dx = y(2 - y)(4 – y)
7. dy/dx = y ln(y + 2)
8. dy/dx = (yey – 9y) / ey
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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