一类一阶非线性微分方程封闭可积条件的统一和推广

The Generalization and Unification About Closed Integrability Conditions of First Order Nonlinear Diffrential Equation of the 1st Kind

给出了一类一阶非线性微分方程:y′=p(x)y+q(x)yμ+r(x)+n∑i=2fi(x)y′的较为广泛的一个封闭可积条件,该条件推广和统一了文献1中的定理1和定理2,特别指出近年来关于著名的Riccati方程和Abei方程可积性的一批最新结果都是它的特例。

The paper is sufficient for first order nonlinear differential equation of the 1 st kind y′=（x）y＋q（x）y^u＋r（x）＋^n∑i=2fi（x）yi to be closed integrability. It generalizes and unifies theorem 1 and theorem 2 in the literature[ 1 ], and explains that some latest results of integrable for wellkown Abel equation and Riccati rquation are special cases of its outcome,