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2. For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) x' = x² – 3x, (b) x' = x(x + 2)², (c) x' = x²(9 — x²).

2. For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) x' = x² – 3x, (b) x' = x(x + 2)², (c) x' = x²(9 — x²).

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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For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions.

(a) x'=x2-3x

(b) x'=x(x+2)2

(c) x'=x2(9-x2)

2. For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) x² = x² – 3x, (b) x' = x(x + 2)², (c) x' = x²(9x²).
Transcribed Image Text:2. For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) x² = x² – 3x, (b) x' = x(x + 2)², (c) x' = x²(9x²).
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