摘要
微分方程是数学的重要分支,但现有方法只能对少数非线性微分方程进行求解。因此,研究提出了采用弹性理论的非线性微分方程求解方法,通过弹性变换法,非线性微分方程可转换为线性微分方程,再逆向进行求解。举例论证表明,弹性变换法能够将高阶或低阶非线性微分方程进行降阶或升阶处理,将其转换为能够求出通解的线性微分方程,最终求出非线性微分方程的通解。由此可得,弹性变换法能够有效提升微分方程的可解类,为解决各领域的实际问题寻找初值条件提供了铺垫。
Differential equations are an important branch of mathematics,but existing methods can only solve a few nonlinear differential equations.Therefore,a nonlinear differential equation solving method based on elastic theory is proposed.Through elastic transformation method,the nonlinear differential equation can be converted into linear differential equation and then solved in reverse.The example illustrates that the elastic transformation method can reduce or raise the order of high-order or low-order nonlinear differential equations,transforming them into linear differential equations that can be solved for the general solution.This ultimately leads to the solution of the nonlinear differential equation.Therefore,the elastic transformation method can effectively expand the class of solvable differential equations,laying the foundation for finding initial conditions for solving real-world problems in various fields.
作者
丁李
DING Li(Huaibei Vocational and Technical College,Huaibei Anhui 235000,China)
出处
《佳木斯大学学报(自然科学版)》
2025年第7期177-180,共4页
Journal of Jiamusi University:Natural Science Edition
基金
安徽省高等学校自然科学重点研究项目(2024AH051703)。
关键词
弹性变换
微分方程
弹性升阶
弹性降阶
可解类
elastic transformation
differential equation
elastic step-up
elastic step-down
solvable class
