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Differential Equations

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Moderate

Finding Solution to the Initial Value Problem, X(0) = ( 5 3)

DIFFEQ-LK01YG

Which is a particular solution to the initial value problem:

$$X'=\left(\begin{array}{cc} 3 & -1 \\\ 5 & -3\end{array}\right)X, \ X(0)=\left(\begin{array}{c} 5 \\\ -3\end{array}\right)$$

A

$X=\left(\begin{array}{cc}1 \\\ 1\end{array}\right)e^{2t}$

B

$X=\left(\begin{array}{cc}1 \\\ 5\end{array}\right)e^{-2t}$

C

$X=\left(\begin{array}{cc}3 \\\ 3\end{array}\right)e^{2t}+\left(\begin{array}{cc}2 \\\ 10\end{array}\right)e^{-2t}$

D

$X=\left(\begin{array}{cc}2 \\\ 2\end{array}\right)e^{2t}+\left(\begin{array}{cc}-7 \\\ -35\end{array}\right)e^{-2t}$

E

None of the above