Consider the following system. =-9x + 4y dx dt dy 4 dt Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A-1,-8 Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K, (2,5) K₂ (4.1) (x(e), y(t)) x X Find the general solution of the given system. - ((20₁0² 50₂) + (40₂0 ¹,₂0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following system.
λ =
dx
dt
dy
4
dt
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
=-9x + 4y
Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.)
K₁=(2,5)
K₂=(4,1)
(x(t), y(t)) =
x
Find the general solution of the given system.
((2₁e5c₂e¹) + (4c₂e-St,cne-st))
Transcribed Image Text:Consider the following system. λ = dx dt dy 4 dt Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) =-9x + 4y Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K₁=(2,5) K₂=(4,1) (x(t), y(t)) = x Find the general solution of the given system. ((2₁e5c₂e¹) + (4c₂e-St,cne-st))
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