On integration of the first order differential equations in a finite terms

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Malykh, M.D.^1,2

Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow

117198, Russia^1

Moscow State University Materials Science Department, Leninskie Gory, Moscow

119991, Russia^2

关键词: First order differential equation;    General solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012026/pdf
DOI  :  10.1088/1742-6596/788/1/012026

来源: IOP

【 摘 要 】

There are several approaches to the description of the concept called briefly as integration of the first order differential equations in a finite terms or symbolical integration. In the report three of them are considered: 1.) finding of a rational integral (Beaune or Poincaré problem), 2.) integration by quadratures and 3.) integration when the general solution of given differential equation is an algebraical function of a constant (Painlevé problem). Their realizations in Sage are presented.