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Differential Equations

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Finding Solution to the System of Differential Equations 11

DIFFEQ-X9JLT4

Find the general solution to the system:

$$X'=\left(\begin{array}{cc} -8 & -1 \\\ 16 & 0\end{array}\right)X$$

A

$X=c_{1}\left(\begin{array}{c} 1 \\\ -4\end{array}\right)e^{-4t}+c_{2}\left(\begin{array}{c} 1 \\\ -4\end{array}\right)te^{-4t}$

B

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

C

$X=c_{1}\left(\begin{array}{c} 1 \\\ -4\end{array}\right)e^{4t}+c_{2}\left(\begin{array}{c} 1 \\\ -4\end{array}\right)te^{4t}$

D

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

E

None of the above