Question:

The differential equation describing the electric current i $=$ i$($t$)$ for an RLC circuit is given by:

Ldtdi$+$Ri$+(1/$C$)*$i$($$)$d$=$E$($t$)($integral $0$ to t$)$

where L$=0\mathrm{.}1,$ R $=3,$ C $=0\mathrm{.}05,$ and E$($t$)=100($u$\_1($t$)-$ u$\_2($t$)),$ with initial conditions q$(0)=0$ and i$(0)=0.$

Using the Laplace transform, solve for i$($t$)$i$($t$).$ Do not convert the given equation into a second$-$order differential equation. Show all steps in detail.