The system can be rewritten as the matrix equation 5 2 Find the General Solution of the System of Differential Equations by 1. Finding the Eigenvalues for the matrix. 2. Find the 2 Eigenvectors of the matrix. 3. Use your Eigenvalues and Eigenvectors to write the General Solution of the System. (A sin(1) cos(4 1) + sin(1) 2 + sin(t) cos(17 t) - sin(17 t) + C, (17t) + sin(171) 14 17 14 -8' cos(17 t) 14 -81 sin(17 t) E

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 28CM
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q8

The system can be rewritten as the matrix equation
6.
5 2
y
Find the General Solution of the System of Differential Equations by
1. Finding the Eigenvalues for the matrix.
2. Find the 2 Eigenvectors of the matrix.
3. Use your Eigenvalues and Eigenvectors to write the General Solution of the System.
- 1
(A
cos(4 1)
sin(t)
C, e cos(4 1)
+ sin(t)
-
cos(t)
|- sin(t)
2.
C,et cos(1)
+ sin(t)
- 1
7r
+
7
1
1
sin (17t)
- 17
-81 cos(17 t)
-8r
D
cos(17 t)
+ C,e
+ sin(17 t)
14
14
17
1
-81 cos(17 t)
+ C,e
14
-81 sin(17 t)
E
C,
17
1
F
+ C,e"
Transcribed Image Text:The system can be rewritten as the matrix equation 6. 5 2 y Find the General Solution of the System of Differential Equations by 1. Finding the Eigenvalues for the matrix. 2. Find the 2 Eigenvectors of the matrix. 3. Use your Eigenvalues and Eigenvectors to write the General Solution of the System. - 1 (A cos(4 1) sin(t) C, e cos(4 1) + sin(t) - cos(t) |- sin(t) 2. C,et cos(1) + sin(t) - 1 7r + 7 1 1 sin (17t) - 17 -81 cos(17 t) -8r D cos(17 t) + C,e + sin(17 t) 14 14 17 1 -81 cos(17 t) + C,e 14 -81 sin(17 t) E C, 17 1 F + C,e"
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