一阶微分方程的积分因子研究

Study on Integral Factor of First Order Differential Equation

随着科学技术的发展,常微分方程在很多学科领域内有着重要的应用,一阶微分方程的求解是整个微分方程求解的根源,我们通常可以使用适当的变量代换把一阶微分方程转化为变量可分离方程,与此同时,还可把一些类型的一阶微分方程转化为恰当微分方程进行求解。本文总结研究一些常见类型的特殊积分因子及其存在的充要条件,从而方便快捷地求出其通解。

With the development of science and technology,ordinary differential equations have important applications in many disciplines.The solution of first-order differential equations is the basis of solving the whole differential equation.The first-order differential equations can be converted into variable separable equations by appropriate variable substitution.In fact,some types of first-order differential equations can also be converted into appropriate differential equations to find the solution.In this paper,some common types of special integral factors and the necessary and sufficient conditions are summarized and studied for their existence,so as to find the general solution conveniently and quickly.