Solution of a Class of Riccati Equations

Abstract: In this paper, we derive the analytical closed form solution of a class of Riccati equations. Since it is well known that to every Riccati equation there corresponds a linear homogeneous ordinary differential equation (ODE), the result obtained is subsequently employed to derive the analytical solution of the class of second order linear homogeneous ODEs corresponding to the class of Riccati equations considered. In addition, we present some examples in order to demonstrate the validity of the results obtained.