near Methods

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Linear Methods

4. Find the general solution of the system of differen-
tial equations
d
X =
dt
14 -4
X
5
10
2 cos(4t) – 4 sin(4t) )
5 cos(4t)
4 cos(4t) + 2 sin(4t)
5 sin(4t)
+ 4t³e!2t
+ 8t'e!2t
Hint: The characteristic polynomial of the coefficient
matrix is (A – 12)² + 4².
Transcribed Image Text:4. Find the general solution of the system of differen- tial equations d X = dt 14 -4 X 5 10 2 cos(4t) – 4 sin(4t) ) 5 cos(4t) 4 cos(4t) + 2 sin(4t) 5 sin(4t) + 4t³e!2t + 8t'e!2t Hint: The characteristic polynomial of the coefficient matrix is (A – 12)² + 4².
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