On Solutions of a Class of Ricatti Equations

The problem discussed in this thesis is concerned with the solutions of a class of Ricatti equations. A method of obtaining closed-form solutions of these first order non-linear differential equations is presented. The algebraic structure of a second order linear differential equation is studied, and it is shown that its solution can be expressed as the product of infinitesimal transformations with each element of the transformation being a Mobius transformation. The product of the Mobius transformations leads to the solutions of special Ricatti equations as well as to the corresponding differential equations. Six different Ricatti equations are considered, and the solutions and the proofs of the solutions for each equation are presented