Remark: This problem is the case that the coefficient matrix has complex eigenvalues. This case is covered in 4.4. For a system of ODEs in the matrix form: A is a 2 x 2 real matrix with an eigenvalue A=5+3i and one corresponding eigenvector According to the Theorem covered in 4.4. its general solution is in the following form: Here Z-AZ -- (t)=C₁i(t) + C₂ (t) 2₁ - Re(e¹¹), 2₁- Im(e) Here Re() represents the real part of a complex vector. Im() represents the imaginary part of a complex vector. Enter , below: ₁(0)- E₂(t)- Remark: This problem requires using the Euler's formula, check the details covered in 4.4. 1.81 181
Remark: This problem is the case that the coefficient matrix has complex eigenvalues. This case is covered in 4.4. For a system of ODEs in the matrix form: A is a 2 x 2 real matrix with an eigenvalue A=5+3i and one corresponding eigenvector According to the Theorem covered in 4.4. its general solution is in the following form: Here Z-AZ -- (t)=C₁i(t) + C₂ (t) 2₁ - Re(e¹¹), 2₁- Im(e) Here Re() represents the real part of a complex vector. Im() represents the imaginary part of a complex vector. Enter , below: ₁(0)- E₂(t)- Remark: This problem requires using the Euler's formula, check the details covered in 4.4. 1.81 181
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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Question
![Remark: This problem is the case that the coefficient matrix has complex eigenvalues. This case is covered in 4.4.
For a system of ODEs in the matrix form:
A is a 2 x 2 real matrix with an eigenvalue A=5+3i and one corresponding eigenvector
According to the Theorem covered in 4.4, its general solution is in the following form:
Here
z' = AZ
*-[+]
z(t)=C₁ zi (t) + C₂ (1)
₁ = Re(e), ₁= Im(e)
Here Re() represents the real part of a complex vector. Im() represents the imaginary part of a complex vector.
Enter , below:
₁ (t)-
₂()
Remark: This problem requires using the Euler's formula, check the details covered in 4.4.
181](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0694005b-3cc2-452c-9b75-517869d0a9bb%2Fa91f2c09-41f1-4808-8633-e0e6c42f1854%2Fn595f2d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Remark: This problem is the case that the coefficient matrix has complex eigenvalues. This case is covered in 4.4.
For a system of ODEs in the matrix form:
A is a 2 x 2 real matrix with an eigenvalue A=5+3i and one corresponding eigenvector
According to the Theorem covered in 4.4, its general solution is in the following form:
Here
z' = AZ
*-[+]
z(t)=C₁ zi (t) + C₂ (1)
₁ = Re(e), ₁= Im(e)
Here Re() represents the real part of a complex vector. Im() represents the imaginary part of a complex vector.
Enter , below:
₁ (t)-
₂()
Remark: This problem requires using the Euler's formula, check the details covered in 4.4.
181
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