rovnice={
0==iU[t]+iR1[t],
iR1[t]==iC1[t]+iC2[t],
iC2[t]==iR2[t],
u1[t]-u2[t]==R1*iR1[t],
u3[t]==R2*iR2[t],
iC1[t]==C1*u2'[t],
iC2[t]==C2*(u2'[t]-u3'[t]),
u[t]==u1[t],
u2[0]==0,
u3[0]==0
};

nezname={u1[t],u2[t],u3[t],iU[t],iR1[t],iR2[t],iC1[t],iC2[t]};
soucastky={R1->1, R2->1,C1->1,C2->1};
u[t_]:=1
reseni=DSolve[rovnice/.soucastky, nezname, t];

Plot[u3[t]/.reseni, {t, 0, 50}, PlotRange->All]