Memoir on Integration of Ordinary Differential [1.2ex] Equations by Quadrature

2011/07/30 by Nail H. Ibragimov, Ibragimov, Nail H.
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1108.0089

openalex publication_date 2011/07/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations reducible to algebraic equations is found. It depends on two arbitrary functions. The method for solving all these equations is given. The new class contains the constant coefficient equations and Euler's equations as particular cases.

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