  The spin-1 Ising model with bilinear and biquadratic exchange interactions
and single-ion crystal field is solved on the Bethe lattice using exact
recursion equations. The general procedure of critical properties investigation
is discussed and full set of phase diagrams are constructed for both positive
and negative biquadratic couplings. In latter case we observe all remarkable
features of the model, uncluding doubly-reentrant behavior and ferrimagnetic
phase. A comparison with the results of other approximation schemes is done.
