Consider the 3 first-order systems (1) x = 3x - 2y y = 4x - y (2) x = 3x - 2y y = 2x - 2y (3) x = -2x + y y = x - 2y (a) For each system identify the coefficient matrix and its eigenvalues. (b) Using the information from (a), classify each equilibrium at o for each system according to its type and stability. (c) Use Sage to plot a slope field for each system. (d) For system (3), find the solution to the IVP x(0) = 3, y(0) = 1.
Consider the 3 first-order systems (1) x = 3x - 2y y = 4x - y (2) x = 3x - 2y y = 2x - 2y (3) x = -2x + y y = x - 2y (a) For each system identify the coefficient matrix and its eigenvalues. (b) Using the information from (a), classify each equilibrium at o for each system according to its type and stability. (c) Use Sage to plot a slope field for each system. (d) For system (3), find the solution to the IVP x(0) = 3, y(0) = 1.
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
![Consider the 3 first-order systems
(1)
x = 3x - 2y
y = 4x - y
x = 3x - 2y
ý
= 2x - 2y
(3)
x = -2x + y
y = x - 2y
(a) For each system identify the coefficient matrix and its eigenvalues.
(b) Using the information from (a), classify each equilibrium at o for each system according
to its type and stability.
(c) Use Sage to plot a slope field for each system.
(d) For system (3), find the solution to the IVP x(0) = 3, y(0) = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2de95a9-7418-40a2-888e-db9ed61cabc0%2Fbb48ecca-78c6-411d-9b7b-2231b0a31f1f%2F4heuss9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the 3 first-order systems
(1)
x = 3x - 2y
y = 4x - y
x = 3x - 2y
ý
= 2x - 2y
(3)
x = -2x + y
y = x - 2y
(a) For each system identify the coefficient matrix and its eigenvalues.
(b) Using the information from (a), classify each equilibrium at o for each system according
to its type and stability.
(c) Use Sage to plot a slope field for each system.
(d) For system (3), find the solution to the IVP x(0) = 3, y(0) = 1.
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