Solve the initial value problem given below. In your solving process, make sure to (1) write the system in matrix form; (2) find eigenvalues; (3) find eigenvectors; (4) use initial conditions to find c₁ and c₂, and (5) state your solution. You may work this out by hand or using MATLAB, but are strongly encouraged to do both as a check on your work. dx dt dy dt = x + 3y, = : 3x + y, x (0) = 3 y (0) = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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Solve the initial value problem given below. In your solving process, make sure to (1) write the
system in matrix form; (2) find eigenvalues; (3) find eigenvectors; (4) use initial conditions to
find c₁ and c₂, and (5) state your solution. You may work this out by hand or using MATLAB, but
are strongly encouraged to do both as a check on your work.
dx
dt
dy
dt
= x + 3y,
= : 3x + y,
x(0) = 3
y (0) = 1
Transcribed Image Text:Solve the initial value problem given below. In your solving process, make sure to (1) write the system in matrix form; (2) find eigenvalues; (3) find eigenvectors; (4) use initial conditions to find c₁ and c₂, and (5) state your solution. You may work this out by hand or using MATLAB, but are strongly encouraged to do both as a check on your work. dx dt dy dt = x + 3y, = : 3x + y, x(0) = 3 y (0) = 1
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