某类非线性常微分方程解的形式
The Form of Solution for a Class of Nonlinear Ordinary Differential Equations

作者: 陶晓珍 , 郭艳凤 , 廖媚 , 陈杰玲 :广西科技大学 理学院,广西 柳州;

关键词: F展开法齐次平衡法Riccati方程F-Expansion Method Homogeneous Balance Method Riccati Equation

摘要: 本论文主要应用F展开法求解某类非线性常微分方程的精确解。首先利用相应自变量变换,再通过齐次平衡法的思想确定方程的某种解的形式,应用数学软件Maple进行求解,再结合相应的Riccati方程的解的表达式,得到了该类非线性常微分方程的精确解的表达形式。

Abstract: In this paper, the exact solution of a class of nonlinear ordinary differential equations is solved by using the F-expansion method. Firstly, by using variable transformation, and through the idea of the homogeneous balance method, some forms of solution are given. By application of mathematical software Maple, some solutions are solved combined with the solution of Riccati equation. And forms of the exact solutions of nonlinear ordinary differential equations are obtained.

文章引用: 陶晓珍 , 郭艳凤 , 廖媚 , 陈杰玲 (2017) 某类非线性常微分方程解的形式。 应用数学进展, 6, 243-248. doi: 10.12677/AAM.2017.63029

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