Density of an individual solution and ergodicity of a family of solutions to the equation dη/dξ=P(ξ, η)/Q(ξ, η)

The paper provides a sharpened proof of M. G. Khudai-Verenov 's theorem on the density in C² of solutions to the equation d/d=P/Q on condition that this equation has two singular points at infinity whose characteristic numbers satisfy certain constraints of the incommensurability type.Translated from Matematicheskie Zametki, Vol. 4, No. 6, pp. 741–750, December, 1968.In conclusion, we wish to thank our scientific co-worker E. M. Landis for many discussions of this work, as well as Ya. G. Sinai and M. L. Gerver,whose comments made it possible to improve the first part.