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Differential Equations

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Particular Solution to IVP - 3 -1 1 1

DIFFEQ-GG4CYJ

What is the particular solution to the initial value problem:

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

A

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

B

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

C

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

D

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

E

None of the above