The DARE arises in place of the CARE when studying discrete time systems; it is not obviously related to the differential equation studied by Riccati.
This differential equation, and the Riccati–Bessel solutions, arises in the problem of scattering of electromagnetic waves by a sphere, known as Mie scattering after the first published solution by Mie (1908).
Giordano Riccati was the son of the theoretical mechanician Jacopo Riccati.
Many mathematicians have studied differential equations and contributed to the field, including Newton, Leibniz, the Bernoulli family, Riccati, Clairaut, d'Alembert, and Euler.