常微分方程求积分因子的一个定理及其应用

The Theorem and Its Application for Solving Integrating Factors of Ordinary Differential Equitions

将积分因子满足的偏微分方程改写成其特征方程,从而与常微分方程组的首次积分相联系.利用"可积组合法"来求积分因子,从而使所求常微分方程化成全微分方程.

The partial differential equitions satisfied with integral factors rewrite to its characteristic equitions . Hence, It is related to the first integral of the system of ordinary differential equations . The integrating factors are caculated by the integral combinatorial method. Therefore, the ordinary differential equitions become the complete differential equations.