积分因子的存在性定理及其应用

The Existence Theorem Integrating Factor and Its Application

给出了一阶微分方程M(x,y)dx+N(x,y)dy=0具有形如μ(x,y)=φ(f(x)g(y))的一类积分因子的充分必要条件以及积分因子的计算公式.作为主要结果的应用,讨论了一类特殊微分方程的解法.

The necessary and sufficient condition of existence of integrating factor for the first order differential equation M （x, y） dx ＋ N （x, y） dy = 0 and the calculating formula of integrating factor are obtained. Some applications will present as well.