探讨一阶常微分方程两种积分因子的存在性及其应用

Existence and application of two integrating factors on first order ordinary differential equation

给出了一阶常微分方程M(x,y)dx+N(x,y)dy=0存在形如u(x,y)=(1/(x2+y2)n),u(x,y)=u(xm,yn)积分因子的充要条件,通过举例验证这些方法的有效性.

This paper gives a sufficient and necessary condition of the integral factors： such as u（x,y）=（1/（x^2＋y^2）^n）,u（x,y）=u（x^m,y^n）,and for first order ordinary differential equation M（x,y）dx＋N（x,y）dy=0 dy. At last , some examples are given to verify the effectiveness of these methods.