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In this book the theory of reflecting function is used for the qualitative study of ordinary first order differential equations with polynomial right-hand side, and the quadratic differential system of the second dimension. We build classes of differential equations and systems with the same Poincare mapping. All equations of this class have the same number of periodic solutions. The initial data of these solutions coincide for such systems. The book is intended for specialists in the field of the qualitative theory of differential equations. It can be used by graduate and undergraduate students in related disciplines.