ABSTRACT
For several reasons, a differential equation of the form of Equation 14.1, and generalizations thereof comprise a highly significant class of nonlinear ordinary differential equations. First, they are intimately related to ordinary linear homogeneous differential equations of the second order. Second, the solutions of Equation 14.1 possess a very particular structure in that the general solution is a fractional linear function in the constant of integration. In applications, Riccati differential equations appear in the classical problems of the calculus of variations and in the associated disciplines of optimal control and filtering.
