The authors summarize the relevant literature on closed-form solutions to the Riccati equation. They describe Kovacic's important contributions to the field. Next, they summarize some of the relevant aspects of the Cox-Ingersoll-Ross model. They describe in more detail the connection between the Riccati equation and practical implementation of the CIR model. They also show that the basic intuition of an analytical solution that has been proposed in the finance literature by \textit{F. Jamshidian} [Appl. Math. Finance 3, 93--115 (1996; Zbl 1097.91525)] ties in closely with the definition proposed for closed-form solutions. They give an explicit example of a new implementation of the extended CIR model that they developed using the ideas in this paper.