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Статья

Malykh, M.D.
On Integration in Quadratures of the First-Order Ordinary Differential Equations / M.D.Malykh. – Text : electronic // Mathematical Modelling and Geometry. – 2025. – Vol. 13, No. 2. – P. 16-31. – URL: https://doi.org/10.26456/mmg/2025-1322. – Bibliogr.: 23.

The first order differential equations of the form pdx + qdy = 0 with algebraic functions p and q of variables x and y are considered. Founded on M. Singer theorem theory of symbolical integration of differential equations is stated with the help of S- and P- Volterra integrals. It is shown that the integrating factor is always P-integral and the integral of the differential equation is S-integral. Calculation of the integrating factor is reduced to the search of an algebraic solution of some quasilinear partial differential equation.



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