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Differential Equations

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Finding the General Solution 2

DIFFEQ-7N1TGD

The general solution to the system of linear differential equations $X'(t)=AX(t)$ where $A$ is given by $A=\left( \begin{array}{cc} 2 & 1 \\\ 1 & 2 \end{array} \right)$ is:

A

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

B

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

C

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

D

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