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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) x² = x²-3x, (b) x² = x(x + 2)², (c) x² = x²(9-x²).

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) x² = x(x + 2)², (c) x² = 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) r' = x²-3x, (b) x² = x(x + 2)², (c) x' = x²(9-x²).
Transcribed Image Text: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) r' = x²-3x, (b) x² = x(x + 2)², (c) x' = x²(9-x²).
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