ClearAll["Global`*"];

iD[uD_]:=(10^(-7))*((E^(19uD))-1);
Plot[iD[uD],{uD,-1,1},PlotRange->{Automatic,{-0.1,3}},PlotStyle->Thick,AxesLabel->{"uD[V]","iD[A]"}];
R2=1000;
R1=1000;
uin=Sin[2*Pi*t];
A=10000;

rcediody={iD1[t]==iD[uout[t]-u4[t]],
iD2[t]==iD[uminus[t]-u4[t]],
iD3[t]==iD[u3[t]-uminus[t]],
iD4[t]==iD[u3[t]-uout[t]]
};
rceproudy={ioz[t]+iD4[t]==iD1[t],
iD1[t]+iD2[t]==iR2[t],
iD3[t]==iD2[t]+iR1[t],
iR2[t]==iD4[t]+iD3[t]
};
rezistory={iR2[t]*R2==u4[t]-u3[t],
iR1[t]*R1==uminus[t]
};
rceOZ={uout[t]==A*(uin-uminus[t])};
rceDohr=Union[D[rcediody,t],rceproudy,rceOZ,rezistory];
nezname=Union[Cases[rceDohr,_Symbol[t],{0,∞}]];
pocs=Union[Cases[rceDohr,a_'[t]:>a[0]==0,{0,∞}]];
pocs=nezname/.{a_[t]:>a[0]==0};
tmax=1;
res=NDSolve[Union[rceDohr,pocs],nezname,{t,0,tmax}][[1]];
Plot[u4[t]-u3[t]/.res,{t,0,tmax}]