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21 2i with vi = -4 + 5i and = -2i with U2 -4 – 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 3-). 1 x(t) t e^(2i) e^(2i) y(t) e -4 5i 1 ). + c2 e^(-2i) + e^(2i) -4 5i B. In fundamental matrix form: cos(2t) sin(2t) x(t) %3D y(t). -4cos(2t)-5sin(2t) -4cos(2t)+5sin(2t) C. As two equations: (write "c1" and "c2" for cq and c2 ) x(t) = c1cos(2t)+c2sin(2t) y(t) = -5c1sin(2t)-4c2cos(2t)

21 2i with vi = -4 + 5i and = -2i with U2 -4 – 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 3-). 1 x(t) t e^(2i) e^(2i) y(t) e -4 5i 1 ). + c2 e^(-2i) + e^(2i) -4 5i B. In fundamental matrix form: cos(2t) sin(2t) x(t) %3D y(t). -4cos(2t)-5sin(2t) -4cos(2t)+5sin(2t) C. As two equations: (write "c1" and "c2" for cq and c2 ) x(t) = c1cos(2t)+c2sin(2t) y(t) = -5c1sin(2t)-4c2cos(2t)

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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Suppose that the matrix A has the following eigenvalues and eigenvectors:

1 21 = 2i with vị = -4 + 5i and = -2i with v2 = -4 – 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: ). x(t) t = C1 e^(2i) e^(2i) y(t) -4 5i e^(-21) + e^(2i) e -4 5i B. In fundamental matrix form: cos(2t) sin(2t) x(t) y(t), -4cos(2t)-5sin(2t) -4cos(2t)+5sin(2t) C. As two equations: (write "c1" and "c2" for cq and c2 ) x(t) = = c1cos(2t)+c2sin(2t) y(t) -5c1sin(2t)-4c2cos(2t)
Transcribed Image Text:1 21 = 2i with vị = -4 + 5i and = -2i with v2 = -4 – 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: ). x(t) t = C1 e^(2i) e^(2i) y(t) -4 5i e^(-21) + e^(2i) e -4 5i B. In fundamental matrix form: cos(2t) sin(2t) x(t) y(t), -4cos(2t)-5sin(2t) -4cos(2t)+5sin(2t) C. As two equations: (write "c1" and "c2" for cq and c2 ) x(t) = = c1cos(2t)+c2sin(2t) y(t) -5c1sin(2t)-4c2cos(2t)
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