一阶常微分方程积分因子解法

利用积分因子求解常微分方程是解方程常用的有效方法,在理论和实践中有着重要地位。惯常的积分因子解法主要讨论两种特殊情况,一种是求只显含自变量的积分因子,另一种是求只显含未知变量的积分因子。本文在未限定变量的条件下,探讨并总结了常微分方程积分因子解法,文中结果拓展总结了求常微分方程积分因子的相关结论与方法。

FURTHER DISCUSSION ON THE METHODS FOR OBTAINING INTEGRATING FACTORS OF THE FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

Using integrating factors to solve ordinary differential equations is an effective method used to solve equations, which plays an important role in theory and practice. Usually, there are two cases of considering to obtain integrating factors of ordinary differential equations. In one case, integrating factors with the independent variable are considered. In the other case, integrating factors with the dependent variable are considered. In the paper, the method to obtain integrating factors of the first order ordinary differential equations is considered in the case of unqualified variables. The sufficient conditions of the existence of integrating factors of the equations are shown, and the methods for obtaining the integrating factors are given. The results in this paper extend and summarize the relevant conclusions and methods of obtaining integrating factors of ordinary differential equations.