PageHeader : Funkcialaj Ekvacioj, 9 (1966), 251-259 Title : On Conditions for an Ordinary Diff.erential Equation Title : of the First Order to be Reducible to a Riccati Title : Equation by a Rational Transformation AuthorInfo : By Tosihusa KIMURA AuthorInfo : (University of Tokyo) section : 1. Introduction. section : 2. Solutions with n branches around their movable branch points. section : 3. Linear relations between $\phi_{1}$ , , $\phi_{n}$ . section : 4. System of differential equations for $\emptyset 1$ , , $\phi_{n}$ . section : 5. Simultaneous system of differential equations and linear relations. section : 6. Theorem. section : 7. Generalization of the Painleve's theorem. section : 8. Generalization of the Malmquist's theorem. section : References