Riccati-Type Equations Associated with Higher Order Ordinary Differential Equations

Abstract

It is shown, similarly as the solution of the Riccati equation can be given via quotients of two linear independent solutions of the second order ordinary differential equation, the solution of the Riccati-Abel differential equation is presented by three linear independent solutions of the third order ordinary differential equation. The method is extended to the class of generalized Riccati-type equations governed by the characteristic polynomials of the associated higher order ordinary differential equations. An explicit functional dependence between solutions of the higher degree Riccati equations with the linear independent solutions of the associated ordinary differential equations established.