The general solution to the semiclassical back-reaction equations for conformally invariant quantum free fields is found in spatially flat homogeneous and isotropic spacetimes containing an unquantized Dirac field and cosmological constant when the ratio of the renormalization parameters is . It shows two-parameter families of bouncing solutions which avoid the singularity. There are several one-parameter families without particle horizons. The stability of the solutions which have a final de Sitter stage is investigated.