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Differential Equations

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Linear System with Repeated Eigenvalues: An IVP

DIFFEQ-QJUZ3S

$x'=Ax$, $x(0)=\left(\begin{array}{c} 2\\\ 1\end{array}\right)$ where:

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

The solution is

A

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

B

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

C

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

D

$x(t)=-e^{2t}\left(\begin{array}{c} 1\\\ -1\end{array}\right) -3e^{2t}\left(\begin{array}{c} t-1\\\ -t\end{array}\right)$