A novel recipe for exactly solving in finite terms a class of special
differential Riccati equations is reported. Our procedure is entirely
based on a successful resolution strategy quite recently applied to
quantum dynamical time-dependent SU(2) problems. The general
integral of exemplary differential Riccati equations, not previously
considered in the specialized literature, is explicitly determined to
illustrate both mathematical usefulness and easiness of applicability
of our proposed treatment. The possibility of exploiting the
general integral of a given differential Riccati equation to solve an
SU(2) quantum dynamical problem, is succinctly pointed out.