  Using the Hubbard representation for $SU(2)$ we write the time-evolution
operator of a two-level system in the disentangled form. This allows us to map
the corresponding dynamical law into a set of non-linear coupled equations. In
order to find exact solutions, we use an inverse approach and find families of
time-dependent Hamiltonians whose off-diagonal elements are connected with the
Ermakov equation. The physical meaning of the so-obtained Hamiltonians is
discussed in the context of the nuclear magnetic resonance phenomenon
