First order equations without mobile critical points (Q5950743)

Let an ordinary differential equation on a function \(w(z)\) be defined in the form \(P(w^\prime,w,z) =0,\) where \(P\) is a polynomial of third degree in \(w^\prime\) with constant principal coefficient and all other coefficients are polynomials in \(w\) and analytic functions in \(z\). The authors explicitly compute conditions on the coefficients of this polynomial under which solutions to the equation have no mobile critical points.