三阶变系数方程许可单参群的一个性质

A Property of the Third-Order Ordinary Differential Equations with Variable Coefficients Admitting One-Parameter Group

在“初始”的三阶变系数线性方程许可某单参群的条件下，考察并获得另一三阶变系数方程许可同一单参群的条件。证明了如果一辅助的二阶线性方程有精确解，则这两个三阶方程在许可同一单参群时也可积。给出了一些例子。

Under the assumption of the initial third-order linear differential equation with variable coefficients admitting a one-parameter group, the conditions of admitting the same one-parameter group for another third-order linear differential equation are discussed. It was showed that if an auxiliary second-order differential equation has exact solutions. these two third-order differnential equations are integrable when they admit the same one-parameter group. Examples are given.