ClearAll["Global`*"]
;
(* Version 1: I already know the differential equation and all the initial conditions! *)
irule=DSolve[{5.0 i''[t]+100 i'[t] +250 i[t]==0, i[0]==0,i'[0]==2},i[t],t];
i1[i_]=i[t]/.irule[[1]]//Simplify;
Print["(Subscript[i, 1]) = ",i1[t]]
Plot[i1[t],{t,0,1.5}, PlotRange-> {0,0.1}]

ClearAll["Global`*"]
(* Version 2: I only know the original equations (like Ohm's Law) *)
irule=DSolve[{20-v1[t] == 100 i[t],i[t]==(4/1000) v2'[t],v1[t]-v2[t]==5 i'[t] , i[0]==0,v2[0]==10},{i[t],v2[t],v1[t]},t];
i1[t_]=1.0*i[t]/.irule[[1]]//Simplify;
Print["(Subscript[i, 1]) = ",i1[1.0*t]//Expand]
Plot[i1[t],{t,0,1.5}, PlotRange-> {0,0.1}]