You are given the following system of differential equations: dx/dy = 6x + 2y, dy/dt = 2x + 9y You are told that the coefficient matrix is: [6 2] [2 9] and this matrix has eigenvectors: [1] and [-2] [2] [1] and the corresponding eigenvalues of 10 and 5. What is the general solution of this system?
You are given the following system of differential equations: dx/dy = 6x + 2y, dy/dt = 2x + 9y You are told that the coefficient matrix is: [6 2] [2 9] and this matrix has eigenvectors: [1] and [-2] [2] [1] and the corresponding eigenvalues of 10 and 5. What is the general solution of this system?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
You are given the following system of
dx/dy = 6x + 2y, dy/dt = 2x + 9y
You are told that the coefficient matrix is:
[6 2]
[2 9]
and this matrix has eigenvectors:
[1] and [-2]
[2] [1]
and the corresponding eigenvalues of 10 and 5.
What is the general solution of this system?
(options A-E are pictured below)
![e10
elot
est
ख
[ ] = a[2] +¹ +8 [1²] ²
[*] =α [1] •
a
X
cos(10t) + B [²] sin(5t)
cos(5t)
-2
sin(10t) + ß [7²]
1
Y
2
[;)] = a[ 2² ] ¹ + $ [2] ²
elot
5t
1
Y
[]=[]+[] M
elot
est
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7a3efc-b3ca-4051-8db3-5036d847891b%2F794a92ad-e7fa-4789-aaa9-8b86b52436f9%2F2zjxfw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:e10
elot
est
ख
[ ] = a[2] +¹ +8 [1²] ²
[*] =α [1] •
a
X
cos(10t) + B [²] sin(5t)
cos(5t)
-2
sin(10t) + ß [7²]
1
Y
2
[;)] = a[ 2² ] ¹ + $ [2] ²
elot
5t
1
Y
[]=[]+[] M
elot
est
2
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