Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t)\end{array}\right)+C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t)\end{array}\right) $

The Answer of Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t)\end{array}\right)+C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t)\end{array}\right) $

Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t)\end{array}\right)+C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t)\end{array}\right) $

The Answer of Consider the First-Order Homogeneous System of Linear Differential Equations$ \mathbf{x}(t)=C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t)\end{array}\right)+C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t)\end{array}\right) $

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Consider the First-Order Homogeneous System of Linear Differential Equations

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Consider the first-order homogeneous system of linear differential equations
$Consider the first-order homogeneous system of linear differential equations What is the general solution of this system? Here, and are arbitrary real constants. A) \mathbf{x}(t) =C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right) B) \mathbf{x}(t) =C_{1} e^{8 t}\left(\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right) +C_{2} e^{8 t}\left(\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) C) \mathbf{x}(t) =C_{1} e^{-8 t}\left[\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right]+C_{2} e^{-8 t}\left[\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) D) \mathbf{x}(t) =C_{1} e^{2 t}\left(\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right)$
What is the general solution of this system? Here, $Consider the first-order homogeneous system of linear differential equations What is the general solution of this system? Here, and are arbitrary real constants. A) \mathbf{x}(t) =C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right) B) \mathbf{x}(t) =C_{1} e^{8 t}\left(\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right) +C_{2} e^{8 t}\left(\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) C) \mathbf{x}(t) =C_{1} e^{-8 t}\left[\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right]+C_{2} e^{-8 t}\left[\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) D) \mathbf{x}(t) =C_{1} e^{2 t}\left(\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right)$ and $Consider the first-order homogeneous system of linear differential equations What is the general solution of this system? Here, and are arbitrary real constants. A) \mathbf{x}(t) =C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right) B) \mathbf{x}(t) =C_{1} e^{8 t}\left(\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right) +C_{2} e^{8 t}\left(\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) C) \mathbf{x}(t) =C_{1} e^{-8 t}\left[\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right]+C_{2} e^{-8 t}\left[\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right) D) \mathbf{x}(t) =C_{1} e^{2 t}\left(\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right)$ are arbitrary real constants.

A) $\mathbf{x}(t) =C_{1} e^{-2 t}\left[\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{-2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right)$
B) $\mathbf{x}(t) =C_{1} e^{8 t}\left(\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right) +C_{2} e^{8 t}\left(\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right)$
C) $\mathbf{x}(t) =C_{1} e^{-8 t}\left[\begin{array}{l}\sin (2 t) \\ \cos (2 t) \end{array}\right]+C_{2} e^{-8 t}\left[\begin{array}{l}-\cos (2 t) \\ \sin (2 t) \end{array}\right)$
D) $\mathbf{x}(t) =C_{1} e^{2 t}\left(\begin{array}{l}\sin (-8 t) \\ \cos (-8 t) \end{array}\right) +C_{2} e^{2 t}\left[\begin{array}{l}-\cos (-8 t) \\ \sin (-8 t) \end{array}\right)$

Consider the First-Order Homogeneous System of Linear Differential Equations

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