For the first order linear system of ODEs: y' (t) = Ay(t), where a -(23) ²). A = Determined the parameter a such that the matrix A has (a): two distinct eigenvalues; (b): a repeated eigenvalue; (c): a pair of conjugate complex eigenvalues. (d): What is the equilibrium of the system? For the conjugate complex eigenvalues, sketch the graphs of the two components y₁ (t) and y2 (t) against time t; and the phase plot assuming y₁ (0) = 1 and y2 (0) = -1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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For the first order linear system of ODEs: y' (t) = Ay(t), where
a -2
2 0
A =
Determined the parameter a such that the matrix A has (a): two distinct eigenvalues; (b): a repeated
eigenvalue; (c): a pair of conjugate complex eigenvalues. (d): What is the equilibrium of the system? For
the conjugate complex eigenvalues, sketch the graphs of the two components y₁ (t) and y2 (t) against time t;
and the phase plot assuming y₁ (0) = 1 and y2(0) = −1.
Transcribed Image Text:For the first order linear system of ODEs: y' (t) = Ay(t), where a -2 2 0 A = Determined the parameter a such that the matrix A has (a): two distinct eigenvalues; (b): a repeated eigenvalue; (c): a pair of conjugate complex eigenvalues. (d): What is the equilibrium of the system? For the conjugate complex eigenvalues, sketch the graphs of the two components y₁ (t) and y2 (t) against time t; and the phase plot assuming y₁ (0) = 1 and y2(0) = −1.
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