kΩ=1000;
μF=(10^(-6));
mH=0.001;
L=50mH;
R1=10kΩ;
R2=1;
c=5μF;
tTry=(Sqrt[L*c]);
Print["time constant= ",tTry,"  s"]
tmax=8tTry;
Uz=UnitStep[t];

currentEqns={iU[t]==iR1[t],iR1[t]==iC[t]+iL[t],iL[t]==iR2[t]};
componentEqns={Uz==u1[t],u1[t]-u2[t]==R1*iR1[t],iC[t]==c*u2'[t],u2[t]-u3[t]==L*iL'[t],u3[t]==R2*iR2[t]};
initialConds={u2[0]==0,iL[0]==0};
eqnsTogether=Union[currentEqns,componentEqns,initialConds];
aux=Cases[eqnsTogether,_Symbol[t],{0,∞}];
unknowns=DeleteCases[aux,UnitStep[t]]//Union;
Length[Union[currentEqns,componentEqns]];
Length[unknowns];