  Energies of the ground, $\beta$ and $\gamma$ bands as well as the associated
B(E2) values are determined for each even-even isotope of the $^{180-196}$Pt
chain by the exact solutions of some differential equations which approximate
the generalized Bohr-Mottelson Hamiltonian. The emerging approaches are called
the Sextic and Spheroidal Approach (SSA), the Sextic and Mathieu Approach
(SMA), the Infinite Square Well and Spheroidal Approach (ISWSA) and the
Infinite Square Well and Mathieu Approach (ISWMA), respectively. While the
first three methods were formulated in some earlier papers of the present
authors, ISWMA is an inedited approach of this work. Numerical results are
compared with those obtained with the so called X(5) and Z(5) models. A contour
plot for the probability density as function of the intrinsic dynamic
deformations is given for a few states of the three considered bands with the
aim of evidencing the shape evolution along the isotope chain and pointing out
possible shape coexistence.
