On integration of the scalar Riccati equation
Abstract
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.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Advanced Differential Equations and Dynamical Systems
Mathematical functions and polynomials
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1667–1673
- Publication date
- 5 February 2026
- Language
- EN