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Differential Equations

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Moderate

Finding Solution to the System of Differential Equations 2

DIFFEQ-NYKGGM

Find the solution to the initial value problem:

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

A

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

B

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

C

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

D

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

E

None of the above