二阶线性微分方程求解的一个新方法

Hew Method to Solve the Second Order Linear Differential Equation

构想了求解二阶变系数线性微分方程的一个新方法 :分离变量法 .在所给条件下 ,将二阶线性微分方程通过变换将其化为变量可分离方程 ,并指出这种转化所作的函数变换 ,从而得到了变系数二阶线性齐次微分方程的一些新的、实用的可积判据和可积类型 ,推广了前人的可积性结果 。

A new solution to the second variable coefficient linear differential equation is worked out. Under the given conditions, through transforming the second linear differential equation into a variable seperative equation and pointing out the function change in this transformation, the paper obtains some new and practical integrabel criterions and integrabel types of second variable linear differential equation, and thus extends the predecessor's integrabel conclusions and the quadrature range of differential equation.