||The mixed spin-1 and spin-3/2 BC Ising ferromagnetic system is studied on the two-fold Cayley tree by means
of the exact recursion relations. The exact expressions for the magnetization, the quadripolar moment, the Curie
temperature, and the free energy are found, and the phase diagrams are constructed on the Cayley tree with the
coordination numbers q = 3, 4 and 6 for various values of the single-ion anisotropy constants ∆1 = D1/J for spin-1
and ∆2 = D2/J for spin-3/2. The existence of tricritical point is investigated for different values of the coordination
numbers q and the single-ion anisotropy values. Phase diagrams in the plan (kT /J, ∆1 ) are constructed when first
∆1 = ∆2 and second ∆1 = ∆2 for selected values of ∆2 . The thermal dependence of the magnetization is also studied.
The results found are compared with those of other approximate methods.