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Question

# Write the vector formulation for the given system of differential equations.$x _ { 1 } ^ { \prime } = e ^ { 2 t } x _ { 2 } , x _ { 2 } ^ { \prime } + ( \sin t ) x _ { 1 } = 1.$

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The vector formulation for the given system of differential equations is:

$\begin{equation*} \begin{bmatrix} x_1' \\ x_2' \\ \end{bmatrix}=\begin{bmatrix} 0 & e^{2t} \\ -\sin{t} & 0 \\ \end{bmatrix} \cdot \begin{bmatrix} x_1 \\ x_2 \\ \end{bmatrix}+\begin{bmatrix} 0 \\ 1 \\ \end{bmatrix} \end{equation*}$

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