Consider the following system. dx = -9x + 4y dt dy dt -5x + 2y 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Consider the following system.
dx
= -9x + 4y
dt
dy
5
-x + 2y
dt
2
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
λ = -8,1
Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.)
K₁
=
K₂
1,4
=
Find the general solution of the given system.
(x(t), y(t))
=
-8t
²/² c ₁ e ² + 4c₂e-8²,₁ c₁e² + c₂e-
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