Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia1579710.22363/2312-9735-2017-25-2-103-112Research ArticleOn Application of M.N. Lagutinski Method to Integration of Differential Equations in Symbolic Form. Part 1MalykhM DFaculty of Materials Sciences; Department of Applied Probability and Informatics Peoples’ Friendship University of Russia (RUDN University) 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federationmalykhmd@yandex.ruLomonosov Moscow State University1512201725210311214042017Copyright © 2017,2017The method of M.N. Lagutinski (1871-1915) allows to find rational integrals and Darboux polynomials for given differential ring and thus can be used for integration of ordinary differential equations in symbolic form. A realization of Lagutinski method was made under free opensource mathematics software system Sage and will be presented in this article with application for symbolic integration of 1st order differential equations. In the first part of the article basic concepts of the Lagutinski method is briefly stated for polynomials rings. Then this method is applied to search of algebraic integrated curves for given ordinary differential equations of the form d + d with , Q[, ]. It is shown how the Lagutinski method allows to look for curves of the given order or to prove that there are not such curves. In particular questions about the optimization of computations and integration in micronomials are considered. The theory and its realization in Sage are tested on numerous examples from standard for Russia text-book by A.F. Filippov. Some recommendations for optimization of the Lagutinski method usage are made in the conclusion of the article.sagesagemathLagutinski methodalgebraic integral curvessagesagemathметод Лагутинскогоинтегральные алгебраические кривые