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Differential Equations

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Finding the Solution to the Initial Value Problem 8

DIFFEQ-MGKPEP

Find the solution to the initial value problem:

$$X'=\left(\begin{array}{cc}3 & 4 \\\ 3 & 2\end{array}\right) X, \ X(0)=\left(\begin{array}{c} 1 \\\ 1\end{array}\right)$$

A

$X=-7\left(\begin{array}{c}1 \\\ -1\end{array}\right)e^{-t}+2\left(\begin{array}{c}4 \\\ -3\end{array}\right)e^{6t}$

B

$X=\cfrac{3}{7}\left(\begin{array}{c}1 \\\ -1\end{array}\right)e^{-t}+\cfrac{1}{7}\left(\begin{array}{c}4 \\\ 3\end{array}\right)e^{6t}$

C

$X=-\cfrac{1}{7}\left(\begin{array}{c}1 \\\ -1\end{array}\right)e^{-t}+\cfrac{2}{7}\left(\begin{array}{c}4 \\\ 3\end{array}\right)e^{6t}$

D

$X=-3\left(\begin{array}{c}1 \\\ -1\end{array}\right)e^{-t}+\left(\begin{array}{c}4 \\\ -3\end{array}\right)e^{6t}$

E

None of the above