$(15$ points$)$ The circuit in the figure is described by the equation

$\left[\begin{array}{c}{i}_L^{\text{'}}\\ v_C^{\text{'}}\end{array}\right]=\left[\begin{array}{cc}0& \frac{1}{L}\\ -\frac{1}{C}& -\frac{1}{RC}\end{array}\right]\left[\begin{array}{c}{i}_L\\ v_C\end{array}\right]$

where $i_L$ is the current through the inductor $L$ and $v_C$ is the voltage drop across the capacitor $C.$ Find formulas for $i_L$ and $v_C$ when $R=0\mathrm{.}5$ohm,$C=\mathrm{.}25$ farads, $L=1\mathrm{.}5$ henry, the initial current is $0$ amp $,$ and the initial voltage is $9$ volts.