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 nonlinear 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. A physical model with the so-obtained Hamiltonians is discussed in the
context of the nuclear magnetic resonance phenomenon.
