Riccati equations

Abstract

In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

Keywords

• Riccati equations
• Bäcklund transformations
• Bernoulli equations.