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(a) y₁ = 3y₁2y2 y2 = 2y1 - 2y2 (b) y₁= 5y₁ - y2 y₂ = 3y₁ + y2

(a) y₁ = 3y₁2y2 y2 = 2y1 - 2y2 (b) y₁= 5y₁ - y2 y₂ = 3y₁ + y2

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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Problem 1 For the systems below, determine whether the phase plane is best described as a source/unstable node, sink/stable node, saddle, center point/ellipses, spiral source, or spiral sink. Show work to justify your answer. (a) y₁ = 3y₁ – 2y2 y₂ = 2y1 - 2y2 (b) y₁ = 5y₁ — Y2 Y₂ = 3y₁ + y2 (c) y₁ = y₁ - 5y2 Y2 = y₁ - 3y2 (d) y₁ = 2y₁ - 5y2 y2 = Y₁ - 2y2 (e) y₁ = 3y₁2y2 y₂ = 4y₁ - y2
Transcribed Image Text:Problem 1 For the systems below, determine whether the phase plane is best described as a source/unstable node, sink/stable node, saddle, center point/ellipses, spiral source, or spiral sink. Show work to justify your answer. (a) y₁ = 3y₁ – 2y2 y₂ = 2y1 - 2y2 (b) y₁ = 5y₁ — Y2 Y₂ = 3y₁ + y2 (c) y₁ = y₁ - 5y2 Y2 = y₁ - 3y2 (d) y₁ = 2y₁ - 5y2 y2 = Y₁ - 2y2 (e) y₁ = 3y₁2y2 y₂ = 4y₁ - y2
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answer c,d,e

Problem 1 For the systems below, determine whether the phase plane is best described as a source/unstable node, sink/stable node, saddle, center point/ellipses, spiral source, or spiral sink. Show work to justify your answer. (a) y₁ = 3y₁ – 2y2 y₂ = 2y1 - 2y2 (b) y₁ = 5y₁ — Y2 Y₂ = 3y₁ + y2 (c) y₁ = y₁ - 5y2 Y2 = y₁ - 3y2 (d) y₁ = 2y₁ - 5y2 y2 = Y₁ - 2y2 (e) y₁ = 3y₁2y2 y₂ = 4y₁ - y2
Transcribed Image Text:Problem 1 For the systems below, determine whether the phase plane is best described as a source/unstable node, sink/stable node, saddle, center point/ellipses, spiral source, or spiral sink. Show work to justify your answer. (a) y₁ = 3y₁ – 2y2 y₂ = 2y1 - 2y2 (b) y₁ = 5y₁ — Y2 Y₂ = 3y₁ + y2 (c) y₁ = y₁ - 5y2 Y2 = y₁ - 3y2 (d) y₁ = 2y₁ - 5y2 y2 = Y₁ - 2y2 (e) y₁ = 3y₁2y2 y₂ = 4y₁ - y2
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