3. Consider the periodic system y' = A(t)y, 3 -1+ cos? t 3 1-, cost sin t A(t) = 3 -1-sint cos t -1+,sin? t (a) Find eigenvalues of A(t) cos (b) Verify that the function $(t) = (sin) 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?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
icon
Related questions
Question
plz solve a and b hand written
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?
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,