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Consider the systems of differential equations dx dt dy dt = 0.1 -0.4y, = -0.4x + 0.7y. For this system, the smaller eigenvalue is and the larger eigenvalue is Use the phase plotter pplane9.m in MATLAB to determine how the solution curves

Consider the systems of differential equations dx dt dy dt = 0.1 -0.4y, = -0.4x + 0.7y. For this system, the smaller eigenvalue is and the larger eigenvalue is Use the phase plotter pplane9.m in MATLAB to determine how the solution curves

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 systems of differential equations dx dt dy dt = = = = 0.1 -0.4y, For this system, the smaller eigenvalue is and the larger eigenvalue is $0 -0.4x + 0.7y. Use the phase plotter pplane9.m in MATLAB to determine how the solution curves behave. A. All of the solution curves converge towards 0. (Stable node) B. The solution curves converge to different points. C. The solution curves race towards zero and then veer away towards infinity. (Saddle) D. All of the solution curves run away from 0. (Unstable node) The solution to the above differential equation with initial values x (0) = 3, y(0) = 5 is x (t) y(t)
Transcribed Image Text:Consider the systems of differential equations dx dt dy dt = = = = 0.1 -0.4y, For this system, the smaller eigenvalue is and the larger eigenvalue is $0 -0.4x + 0.7y. Use the phase plotter pplane9.m in MATLAB to determine how the solution curves behave. A. All of the solution curves converge towards 0. (Stable node) B. The solution curves converge to different points. C. The solution curves race towards zero and then veer away towards infinity. (Saddle) D. All of the solution curves run away from 0. (Unstable node) The solution to the above differential equation with initial values x (0) = 3, y(0) = 5 is x (t) y(t)
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Step 1: Introduction of the given problem

fraction numerator d x over denominator d t end fraction equals 0.1 x minus 0.4 y fraction numerator d y over denominator d t end fraction equals negative 0.4 x plus 0.7 y x open parentheses 0 close parentheses equals 3 comma space y open parentheses 0 close parentheses equals 5

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