$v=\{\begin{array}{cc}50V,& t0\\ A{e}^{-100t}+B{e}^{-600t}V,& t0\end{array}$

If the capacitor is valued at $4$ mF and has a current $i(0^{+})=2A,$ find:

$($a$)$ The constants A and $B,$

$($b$)$ The energy stored in the capacitor at $t=0.$

$($c$)$ The capacitor current for all $t>0.$