Find formulas for the current $i_L$ and the voltage $v_C$ for the circuit described by the equation below,
assuming $R_1 = 0.4$ ohm, $R_2 = 0.1$ ohm, $C = 0.5$ farad, and $L = 0.1$ henry. The initial current is 0 amp,
and the initial voltage is 4 volts.
$\begin{bmatrix} i'_L \ v'_C \end{bmatrix} = \begin{bmatrix} -\frac{R_2}{L} & -\frac{1}{L} \\ \frac{1}{C} & -\frac{1}{(R_1C)} \end{bmatrix} \begin{bmatrix} i_L \ v_C \end{bmatrix}$
$i_L(t) = \square$ and $v_C(t) = \square$