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Differential Equations

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Finding the General Solution with Repeated Eigenvalues

DIFFEQ-PUL94X

Find the general solution of the system:

$$X'=\left(\begin{array}{cc}1 & -3 \\\ 3 & 7\end{array}\right)X$$

A

$X=c_{1}\left(\begin{array}{c}-3 \\\ 3\end{array}\right)e^{4t}+c_{2}\left(\left(\begin{array}{c} -3 \\\ 3\end{array}\right)t+\left(\begin{array}{c}1 \\\ 0\end{array}\right)\right)e^{4t}$

B

$X=c_{1}\left(\begin{array}{c}-3 \\\ 3\end{array}\right)e^{4t}+c_{2}\left(\begin{array}{c} -3 \\\ 3\end{array}\right)te^{4t}$

C

$X=c_{1}\left(\begin{array}{c}-3 \\\ 3\end{array}\right)e^{4t}+c_{2}\left(\begin{array}{c} 1\\\ 0\end{array}\right)e^{4t}$

D

$X=c_{1}\left(\begin{array}{c}3 \\\ -3\end{array}\right)e^{4t}+c_{2}\left(\left(\begin{array}{c} 3 \\\ -3\end{array}\right)t+\left(\begin{array}{c}1 \\\ 0\end{array}\right)\right)e^{4t}$

E

None of the above