Laplace transforms: Simple Electrical Network

Problem Statement

Using the formulas

$E(t)=L{\dfrac {di_{R}}{dt}}+Ri_{C}$
$RC{\dfrac {di_{R}}{dt}}+i_{R}-i_{C}=0$

Solve the system when V0 = 50 V, L = 0.5 h, R = 60 Ω, C = 10^-4 f, and the currents are initially zero.