Consider the following system. λ = dx dt K₂ = = 5 dy 3 dt 4 Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) 2 x + 4y Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K₁ = = x-3y Find the general solution of the given system. (x(t), y(t)) =

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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8.2(b1) #2

Consider the following system.
λ =
K₂
dx
dt
dy
dt
=
=
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
5
=
x + 4y
Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.)
K₁ =
2
-x - 3y
Find the general solution of the given system.
(x(t), y(t))
Transcribed Image Text:Consider the following system. λ = K₂ dx dt dy dt = = Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) 5 = x + 4y Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K₁ = 2 -x - 3y Find the general solution of the given system. (x(t), y(t))
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