3. Consider the periodic system y' = A(t)y, 3 -1+ cos? t 3 1. - cos t sin t A(t) = 3 -1- sin t cos t -1+ sin't -1+3sin?t (a) Find eigenvalues of A(t) cos (b) Verify that the function (t) = Cos)et/2 is a solution of the equation %3D (c) Compute the multipliers and characteristic exponents of the system (d) Does the system have a periodic solution?
3. Consider the periodic system y' = A(t)y, 3 -1+ cos? t 3 1. - cos t sin t A(t) = 3 -1- sin t cos t -1+ sin't -1+3sin?t (a) Find eigenvalues of A(t) cos (b) Verify that the function (t) = Cos)et/2 is a solution of the equation %3D (c) Compute the multipliers and characteristic exponents of the system (d) Does the system have a periodic solution?
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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Transcribed Image Text:3. Consider the periodic system y' = A(t)y,
3
cos?
2
3
-1-sin t cos t
2
3
1- cos t sin t
2
3
A(t) =
(-1-sin t cost -1+sin't)
(a) Find eigenvalues of A(t)
cos
(b) Verify that the function (t) = ( et/2 is a solution of the equation
(c) Compute the multipliers and characteristic exponents of the system
(d) Does the system have a periodic solution?
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