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

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Question

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?

(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

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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