Write the system $x^{\,\prime} = e^{3t} x - 6t y + 3\sin\!\left(t\right)$,   $y^{\,\prime} = 8\tan\!\left(t\right) y + 3 x - 3\cos\!\left(t\right)$ in the form

$$\frac{d}{dt} \left\lbrack\begin{array}{c} x \\ y \end{array}\right\rbrack = P(t) \left\lbrack\begin{array}{c} x \\ y \end{array}\right\rbrack + \boldsymbol{\vec{f}}(t).$$

Use prime notation for derivatives and write $x$ and $x^{\,\prime}$, etc., instead of $x(t)$, $x^{\,\prime}(t)$, or $\frac{dx}{dt}$.