About some equations of the third order with six poles

Investigating ordinary differential equations of the third order on the subject of belonging to P-type (solutions of such equations have no movable critical singular points), Chazy has built an equation (Chazy equation) with 32 coefficients. If these coefficients satisfy the special (S)-system, then Chazy equation belongs to P-type. In this paper we find three solution of the (S)-system and build three classes of Chazy equation of the P-type.