一阶常微分方程具有一种乘积形式积分因子的求解

The solution of first order ordinary differential equation with the integral factor of a product form

讨论一阶常微分方程M(x,y)dx+N(x,y)dy=0的积分因子问题,给出了方程具有形如f(x+y)g(axt+bys+cxαyβ)的积分因子的充要条件以及求上述积分因子的方法。

This paper discusses the problem of integral factor for the first order ordinary differential equation： M（ x ,y）dx ＋ N（ x ,y）dy = 0, gives a sufficient and necessary condition of integral factor wi~ the form off（x ＋ y）g（ax^i＋by^s＋cx^αy^β） and brings a method for solving the integral factor, Moreover, this paper applies the method to an example.