二阶非线性微分方程的一个新的可解类型

先从物理实例引入了一类新的二阶非线性微分方程，然后对这类方程引进特征方程的概念，运用未知函数变换及自变量变换和初等代数的方法证明了这类非线性微分方程是可解的，且给出了通解的特征根的表达式，从而扩大了常微分方程的可解范围．

A New Solvable Type of Second Order Non-Linear Differential Equation

In this paper, a new type of second order non-linear differential equation is first led from physics example, and then the concept of characteristic equation is led into it, then it is proved to that this kind of non-linear differential equation is solvable with the methods of the transformation of unknown function, the transformation of independent, and elementary algebraic. The characteristic root expression formula of its general solution was given, thus the solvable range of ordinary differential equation was extended.