一类新二阶非线性微分方程的可积判据

Integral Criterion of One Kind of New Second Order Non-Linear Differiential Equation

先通过类比著名的Bernoulli方程 ,提出了一类新二阶非线性微分方程 ,然后对它引进特征方程的概念 ,给出了一个实用的可积充分判据及其通解的积分表达式 ;在退化情形下 。

Analogizing the famous Berroulli Equation,one kind of new second order non-linear differiential equation is given.And then,the concept of characteristic equation is introduced,a practical,integral,Sufficient criterion and the integral expression of its general solution for this equation is given.Particularly,the expression of the general solution for the classical second constant coefficient linear non-homogeneous differential equation and a new integral type for the second order variable coefficient linear homogeneous differential equation are deduced.