82 - Riccati Equation

Abstract

This chapter discusses Riccati equation applicable to ordinary differential equations of the form y' = a(x)y2 + b(x)y + c(x). It yields a reformulation as a linear second-order ordinary differential equation, or a second solution if one solution is already known. A change of dependent variable can transform a Riccati equation to a linear second-order ordinary differential equation. Also, if one solution to a Riccati equation is known, then the other solution can be written down explicitly. The chapter describes two procedure for solving the Riccati equation y' = a(x)y2 + b(x)y + c(x). Examples are also presented. The chapter also describes a Riccati transformation.