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Differential Equations

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Finding Solution to the System of Differential Equations 3

DIFFEQ-LXTSX6

Which is a solution to the system:

$$X'=\left(\begin{array}{cc} 0 & -8 \\\ 2 & 0 \end{array}\right)X$$

A

$X=\left(\begin{array}{c} 2 \\\ 0 \end{array}\right)\cos 4t$

B

$X=\left(\begin{array}{c} 2 \\\ 0 \end{array}\right)\cos 4t+\left(\begin{array}{c} 0 \\\ -1 \end{array}\right)\sin 4t$

C

$X=\left(\begin{array}{c} 0 \\\ -1 \end{array}\right)\sin 4t$

D

$X=\left(\begin{array}{c} 2 \\\ 0 \end{array}\right)\sin 4t-\left(\begin{array}{c} 0 \\\ -1 \end{array}\right)\cos 4t$

E

None of the above