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3. Consider the periodic system y' = A(t)y, -1+ 0t 1-ost sin |-1- sint cost ) 3 cos2 2 3 3 A(t) = 2 3 -1+ sin?t 2 (a) Find eigenvalues of A(t) cos (b) Verify that the function (t) = (n et/2 is a solution of the equation

3. Consider the periodic system y' = A(t)y, -1+ 0t 1-ost sin |-1- sint cost ) 3 cos2 2 3 3 A(t) = 2 3 -1+ sin?t 2 (a) Find eigenvalues of A(t) cos (b) Verify that the function (t) = (n et/2 is a solution of the equation

Advanced Engineering Mathematics
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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hand written plz a and b part only
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?
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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