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Differential Equations

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Moderate

Finding Solution to the System of Differential Equations 8

DIFFEQ-YVGKRE

Which is not a solution to the system:

$$X'=\left(\begin{array}{cc} 1 & 5 \\\ -4 & -7 \end{array}\right)X$$

A

$X=\left[\left(\begin{array}{c} 5 \\\ -4\end{array}\right)\cos 2t-\left(\begin{array}{c} 0 \\\ 2\end{array}\right) \sin 2t\right] e^{-3t}$

B

$X=\left[\left(\begin{array}{c} 5 \\\ -4\end{array}\right)\sin 2t+\left(\begin{array}{c} 0 \\\ 2\end{array}\right) \cos 2t\right] e^{-3t}$

C

$X=\left[\left(\begin{array}{c} 5 \\\ -2\end{array}\right)\sin 2t+\left(\begin{array}{c} 5 \\\ -6\end{array}\right) \cos 2t\right] e^{-3t}$

D

$X=\left[\left(\begin{array}{c} 5 \\\ -4\end{array}\right)\cos 2t+\left(\begin{array}{c} 0 \\\ 2\end{array}\right) \sin 2t\right] e^{-3t}$

E

$X=\left[\left(\begin{array}{c} 10 \\\ -8\end{array}\right)\sin 2t+\left(\begin{array}{c} 0 \\\ 4\end{array}\right) \cos 2t\right] e^{-3t}$