Exact parametric solutions of the nonlinear Riccati ODE as well as of some relative classes of linear second order ODEs of variable coefficients

Abstract

We present a methodology for constructing the exact parametric or closed form solutions of the nonlinear first order Riccati ordinary differential equation (ODE) and other equivalent class of second order linear ODEs with variable coefficients. For illustration purposes we extract the general solutions of the strongly nonlinear first order kinematic Euler’s ODEs describing the dynamics of a rigid-body free to rotate about a fixed point.