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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
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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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.
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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