A note about a new method for solving Riccati differential equations

Abstract

Al Bastami, Belić, and Petrović (2010) proposed a new method to find solutions to some Riccati differential equations. Initially, they obtain a second-order linear ordinary differential equation (ODE) through a standard variable change in the Riccati equation. They then propose a new variable change and discuss the resolution of the resulting ODE in two cases. In the first one, the resulting ODE has constant coefficients. In the second case, they claim that it is possible to arbitrarily choose one of the resulting ODE coefficients and solve particular Riccati ODEs. We show in this work that all Riccati equations that belong to the first case can also be solved by Chini’s method. Furthermore, we show that any Riccati equation fits the second case and that the choice of the resulting ODE coefficients is not free.