Differential Equations

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Which is a Solution 2

DIFFEQ-J6GK5X

Which is a solution to the system:

$$X'=\left(\begin{array}{ccc} 0 & -1 & 0 \\\ 1 & 0 & 0 \\\ 0 & 0 \\\ 2\end{array}\right)X$$

A

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

B

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

C

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

D

$X=\left(\begin{array}{c} 0 \\\ 1 \\\ 0 \end{array}\right) e^{2t}$

E

None of the above