Although the scalar Riccati equation has been studied extensively, explicit solution methods are known only for miscellaneous special cases. Using recent techniques related to the one-dimensional Schrödinger equation, we establish a new condition under which the scalar Riccati equation can be solved explicitly. The solution differs qualitatively from previous methods in that it involves neither Bessel functions nor elementary combinations of quadratures.
Peter C. Gibson (Thu,) studied this question.