Chapter 5.7, Problem 22E

[M] The circuit in the figure is described by the equation

$\left[\begin{array}{c}{i^{\prime }}_L\\ {v^{\prime }}_{{}_C}\end{array}\right]=\left[\begin{array}{cc}0& 1/L\\ -1/C& -1/(R_{1}C)\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{i}_L\\ v_C\end{array}\end{array}\right]$

where it 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 = .5 ohm, C = 2.5 farads, L = .5 henry, the initial current is 0 amp, and the initial voltage is 12 volts.