Open AccessElastic transformation method for solving ordinary differential equations with variable coefficients
Author(s) -
Pengshe Zheng,
Jun Luo,
Shunchu Li,
Xiaoxu Dong
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022077
Subject(s) - mathematics , ordinary differential equation , collocation method , mathematical analysis , exact differential equation , separable partial differential equation , variable (mathematics) , integrating factor , differential equation , examples of differential equations , transformation (genetics) , differential algebraic equation , l stability , laguerre polynomials , biochemistry , chemistry , gene
Aiming at the problem of solving nonlinear ordinary differential equations with variable coefficients, this paper introduces the elastic transformation method into the process of solving ordinary differential equations for the first time. A class of first-order and a class of third-order ordinary differential equations with variable coefficients can be transformed into the Laguerre equation through elastic transformation. With the help of the general solution of the Laguerre equation, the general solution of these two classes of ordinary differential equations can be obtained, and then the curves of the general solution can be drawn. This method not only expands the solvable classes of ordinary differential equations, but also provides a new idea for solving ordinary differential equations with variable coefficients.