International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 205-207

Riccati equations

Lloyd K. Williams

Department of Mathematics, Texas Southern University, Houston 77004, Texas, USA

Received 2 February 1986

Copyright © 1987 Lloyd K. Williams. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.