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For the system of differential equations, 6 - 5 18 16 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = = U1 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂

For the system of differential equations, 6 - 5 18 16 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. A1, A2 = = U1 = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. U2 = y' = y(t) d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. = C1 + c₂

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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For the system of differential equations, a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) = A1, A2 = y' U1 = = b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U2 = - 5 6 18 16 c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. y(t) = C1 + c₂
Transcribed Image Text:For the system of differential equations, a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) = A1, A2 = y' U1 = = b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U2 = - 5 6 18 16 c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂. Enter the eigenvectors as a matrix with an appropriate size. d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)v₁ + c₂f2(t)v₂. y(t) = C1 + c₂
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