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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
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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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
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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