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Differential Equations

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Which is a Solution

DIFFEQ-HEPJFL

Which is a solution to the system:

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

A

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

B

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

C

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

D

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

E

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