Consider the following linear system of differential equations: x' : y' = =X- - Y = -X 4y Write this system in matrix vector form. Show that X(t) = [2e + cos(21)] sin(2t) B tem of differential equations. is a solution of this sys- C Write the solution above as scalar x(t) and y(t) solutions without matrices or vectors.
Consider the following linear system of differential equations: x' : y' = =X- - Y = -X 4y Write this system in matrix vector form. Show that X(t) = [2e + cos(21)] sin(2t) B tem of differential equations. is a solution of this sys- C Write the solution above as scalar x(t) and y(t) solutions without matrices or vectors.
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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![### Differential Equations and Systems
Consider the following linear system of differential equations:
\[ x' = -x - 4y \]
\[ y' = x - y \]
**A.** Write this system in matrix-vector form.
**B.** Show that \( \mathbf{X}(t) = \begin{bmatrix} 2e^{-t} \cos(2t) \\ e^{-t} \sin(2t) \end{bmatrix} \) is a solution of this system of differential equations.
**C.** Write the solution above as scalar \( x(t) \) and \( y(t) \) solutions without matrices or vectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ba71b9f-6645-4b82-be5d-cda1c9d5ec57%2F35c97941-4f1d-4abb-be65-787ef9913d25%2F2l7puu7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Differential Equations and Systems
Consider the following linear system of differential equations:
\[ x' = -x - 4y \]
\[ y' = x - y \]
**A.** Write this system in matrix-vector form.
**B.** Show that \( \mathbf{X}(t) = \begin{bmatrix} 2e^{-t} \cos(2t) \\ e^{-t} \sin(2t) \end{bmatrix} \) is a solution of this system of differential equations.
**C.** Write the solution above as scalar \( x(t) \) and \( y(t) \) solutions without matrices or vectors.
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