Consider the systems of differential equationsdxdtdydt====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 curvesbehave.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 isx (t)y(t)

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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

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 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)

Expert Solution

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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in pic
Everything we've done with systems of 2 linear, constant co- efficient, homogeneous differential equations works for larger systems as well. Ask wolframalpha.com for the eigenvalues and eigenvectors of the following system of three differential equations, and use the result to write the general solution: -2 -4 2 *m-Biss X' (t) -2 1 2 X(t) 4 2 5 =