R1=100;
L=0.1;
R2=200;
c=100*(10^(-6));
uz[t_]=10;
u1[t]=-uz[t];
u1[0]=-uz[0];
u1'[t]=-uz'[t];
Nodeqns={i3[t]==i2[t]+i1[t],i1[t]+i2[t]==i5[t]+i4[t]};
Parteqns={i2[t]==c*D[u1[t]-u2[t],t],i1[t]*R1==u1[t]-u2[t],u2[t]==R2*i5[t],u2[t]==L*i4'[t]};
Manipulate[
initials={u1[0]-u2[0]==u20,i4[0]==i40};
eqns=Union[Nodeqns,Parteqns,initials];
vars=Cases[eqns,_Symbol[t],{0,∞}]//Union;
tmax=0.2;
sol=NDSolve[eqns,vars,{t,0,tmax},StartingStepSize->(10^(-9))][[1]];
Plot[i4[t]/.sol,{t,0,tmax},PlotRange->{Automatic,{-0.5,0.2}},PlotStyle->Thick,AxesLabel->{"t[s]","var"}],{i40,-.2,0},{u20,-12,-8}]

SteadyEqns=(Union[Nodeqns,Parteqns]/._'[t]:>0)/.a_[t]:>a
Solve[SteadyEqns]//N