Elastic transformation method for solving ordinary differential equations with variable coefficients
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 di...
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Published in | AIMS mathematics Vol. 7; no. 1; pp. 1307 - 1320 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
AIMS Press
01.01.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2473-6988 2473-6988 |
DOI: | 10.3934/math.2022077 |