一阶常微分方程有形如μ(ax~α+bx^sy^l+cy~β)积分因子的充要条件

A Sufficient and Necessary Condition of Integral Factor Such As μ(ax~α+bx^sy^l+cy~β) for First Order Ordinary Differential Equation

讨论了一阶常微分方程M(x,y)dx+N(x,y)dy=0 的积分因子问题,给出了一阶常微分方程有形如μ(axα+bxsyl+cyβ)的积分因子的一个充分必要条件.推广了相关文献的结果,从而丰富了常微分方程的解法.

This paper discusses the problem of integral factor about the first order constant differential equation: (M(x,y)dx+N(x,y)dy)=0, gives a sufficient and necessary condition of integral factor such as μ(ax~α+bx^sy^l+cy~β) for first order ordinary differential equation, and makes an extension form the conclusion of related reference. The results in this paper perfect the method of solving ordinary differential equation.