Abstract
It is showed in this note that if the Schwarzian differential equation (*) {w, z}=R(z, w)=P(z, w)/Q(z, w), where P(z, w) and Q(z, w) are polynomials in w with meromorphic coefficients, possesses an admissible solution w(z), then w(z) satisfies a first order equation of the form (**) (w')2+B(z, w)w'+A(z, w)=0, where B(z, w) and A(z, w), are polynomials in w having small coefficients with respect to w(z), or by a suitable Möbius transformation (*) reduces into {w, z}=P(z, w)/(w+b(z))2 or {w, z}=c(z). Furthermore, we study the equation (**).
