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Consider the following system. dx dt dy dt = 6x + 5y K = = -2x + 8y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A 7-3i, 7+3i Find an eigenvector corresponding to the eigenvalue with positive imaginary part. Find the general solution of the given system. (x(t), y(t)) =

Consider the following system. dx dt dy dt = 6x + 5y K = = -2x + 8y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A 7-3i, 7+3i Find an eigenvector corresponding to the eigenvalue with positive imaginary part. Find the general solution of the given system. (x(t), y(t)) =

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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Consider the following system. dx dt dy dt = 6x + 5y K = = -2x + 8y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 7-3i, 7 + 3i Find an eigenvector corresponding to the eigenvalue with positive imaginary part. Find the general solution of the given system. (x(t), y(t)) =
Transcribed Image Text:Consider the following system. dx dt dy dt = 6x + 5y K = = -2x + 8y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 7-3i, 7 + 3i Find an eigenvector corresponding to the eigenvalue with positive imaginary part. Find the general solution of the given system. (x(t), y(t)) =
Consider the following system. dx dt dy dt = 8x + 13y K = t = -2x+10y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 9+5i,9 - 5i Find an eigenvector 1 - 5i 2 9 - 5i, 9 + 5i corresponding to the eigenvalue with positive imaginary part. (1 - 5i, 2) X Find the general solution of the given system. (x(t), y(t)) = C₁cos 5t + Сäsin 5t C₁ (cos(5t) +5 sin(5t), 2 cos (5t)) et + C₂ (sin(5t) - 5 cos(5t), 2 sin(5t))eºt X
Transcribed Image Text:Consider the following system. dx dt dy dt = 8x + 13y K = t = -2x+10y Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = 9+5i,9 - 5i Find an eigenvector 1 - 5i 2 9 - 5i, 9 + 5i corresponding to the eigenvalue with positive imaginary part. (1 - 5i, 2) X Find the general solution of the given system. (x(t), y(t)) = C₁cos 5t + Сäsin 5t C₁ (cos(5t) +5 sin(5t), 2 cos (5t)) et + C₂ (sin(5t) - 5 cos(5t), 2 sin(5t))eºt X
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