Liénard and Riccati differential equations related via Lie algebras (Q950599)

The Riccati differential equation of the form \[ \frac{dz}{dx}=A_0(x)+A_1(x)z+A_2(x)z^2 \] is considered, where \(A_i\), \(i=0,1,2\) are continuous functions. The authors show that some Liénard differential equations of the form \[ \ddot{x}+f(x)\dot{x}+g(x)=0, \] \(f,g:\mathbb{R}\to\mathbb{R}\), are real \(C^1\) functions, can be transformed into a Riccati equation using some more general change of variables used in classical Lie theory.