We have seen that a system of two linear homogeneous differential equations with constant coefficients can be written in matrix form as x'= Ax. We have also seen that the general solution to such a system can be written as (1) π = c₁k₁e¹₁t + c₂kzełzt where X₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors. Solve the system of differential equations below and write your answer in the form of equation (1) above. x': [2² x -1810-181-
We have seen that a system of two linear homogeneous differential equations with constant coefficients can be written in matrix form as x'= Ax. We have also seen that the general solution to such a system can be written as (1) π = c₁k₁e¹₁t + c₂kzełzt where X₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors. Solve the system of differential equations below and write your answer in the form of equation (1) above. x': [2² x -1810-181-
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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Homework 16:
Question 3
![We have seen that a system of two linear homogeneous differential equations with constant
coefficients can be written in matrix form as
x'= Ax.
We have also seen that the general solution to such a system can be written as
(1) x = ₁k₁e¹₁ + ₂kze ¹2t
where A₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors.
Solve the system of differential equations below and write your answer in the form of equation (1)
above.
-2 -71
*-[3])
x' =
0
x
-180-180
C1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9086a1c0-d376-4c80-871f-f484ad7b10c1%2F1eba8899-8312-40c1-80ae-2ffc9ac95031%2Fgtb6lyf_processed.png&w=3840&q=75)
Transcribed Image Text:We have seen that a system of two linear homogeneous differential equations with constant
coefficients can be written in matrix form as
x'= Ax.
We have also seen that the general solution to such a system can be written as
(1) x = ₁k₁e¹₁ + ₂kze ¹2t
where A₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors.
Solve the system of differential equations below and write your answer in the form of equation (1)
above.
-2 -71
*-[3])
x' =
0
x
-180-180
C1
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