Movable singularities of equations of Liénard type (Q1045729)

Consider a differential equation of Liénard type \[ y''=F(z,y)y' + G(z,y), \] where \(F\) and \(G\) are polynomials in \(y\). Under the supposition \(\deg_yG \leq \deg_y F+1\) and a certain resonance condition, it is shown that, for a solution \(y(z),\) any movable singularity reachable by a finite length curve is an algebraic branch point. Moreover, an example with the maximum balance condition \(\deg_yG=2\deg_yF +1\) is also discussed, in which a non-algebraic movable singularity occurs.