一类三阶非线性微分方程的可积条件

Integrability Conditions of A Class of Third-order Nonlinear Differential Equation

构造了适当的变换,研究了一类三阶非线性微分方程y+py″+qy′+ry=f(x)(y″-sy′-s1y)n(n≠0)的可积条件,并给出了其通解的积分表达式.

We make up some suitable transformations and study the integrability conditions of a class of thirdorder nonlinear differential equation：y″′＋Py″＋qy′＋ry=f（x）（y″-sy′＋s1y）″ （n≠0,where p,q,r,s, s1, n are constants）. The Integral expression of its general solution of this equation is given.