Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t)\end{array}\right)+C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t)\end{array}\right) $

The Answer of Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t)\end{array}\right)+C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t)\end{array}\right) $

Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t)\end{array}\right)+C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t)\end{array}\right) $

The Answer of Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t)\end{array}\right)+C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t)\end{array}\right) $

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Consider the First-Order Homogeneous System of Linear Differential Equations

Question 45

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Consider the first-order homogeneous system of linear differential equations
$Consider the first-order homogeneous system of linear differential equations The eigenvalues and corresponding eigenvectors for this system are: Which of these is the general solution for this system? A) \mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t) \end{array}\right) +C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right) B) \mathbf{x}(t) =C_{1} e^{t}\left(\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right) +C_{2} e^{t}\left(\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right) C) \mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right) D) \mathbf{x}(t) =C_{1} e^{t}\left\{\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right]$
The eigenvalues and corresponding eigenvectors for this system are:
$Consider the first-order homogeneous system of linear differential equations The eigenvalues and corresponding eigenvectors for this system are: Which of these is the general solution for this system? A) \mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t) \end{array}\right) +C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right) B) \mathbf{x}(t) =C_{1} e^{t}\left(\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right) +C_{2} e^{t}\left(\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right) C) \mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right) D) \mathbf{x}(t) =C_{1} e^{t}\left\{\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right]$
Which of these is the general solution for this system?

A) $\mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}\sin (5 t) \\ -\cos (5 t) \end{array}\right) +C_{2} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right)$
B) $\mathbf{x}(t) =C_{1} e^{t}\left(\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right) +C_{2} e^{t}\left(\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right)$
C) $\mathbf{x}(t) =C_{1} e^{t}\left[\begin{array}{l}-\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right)$
D) $\mathbf{x}(t) =C_{1} e^{t}\left\{\begin{array}{l}\sin (5 t) \\ \cos (5 t) \end{array}\right]+C_{2} e^{t}\left[\begin{array}{l}\cos (5 t) \\ -\sin (5 t) \end{array}\right]$

Consider the First-Order Homogeneous System of Linear Differential Equations

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