i)
r=50; l=5; c=0.05; e=10; q[0]=7; i[0]=3;
IVPforq={l q''[t]+r q'[t]+(1/c) q[t]==e, q[0]==7, q'[0]==3}
ii)
i[t]=q'[t];
Solve[l i'[0]+r i[0]+(1/c) q[0]==e, i'[0]]
IVPfori={l i''[t]+r i'[t]+(1/c) i[t]==0, i[0]==3, i'[0]==-56}
iii)
DSolve[IVPforq, q[t], t];
charge[t]=Chop[N[(q[t]/.%)[[1]]]]
Limit[charge[t],t->Infinity]0.5
iv)
DSolve[IVPfori, i[t], t];
current[t]=Chop[N[(i[t]/.%)[[1]]]]
Limit[current[t],t->Infinity]0