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