二阶变系数线性微分方程的几个可积类型

Several integrable forms of two-order Variable coefficient linear differential equations

论文【1】给出了一些变系数线性微分方程的可积类型,资料【2,3】利用“连锁法”也给出了一些变系数性微分方程的可积类型,而【2,3】的结果包括了【1】的结果。

In this paper, some conditions of reducing the second order linear ordinary differential equations with variable coefficients to those with constant coefficients are given, by means of the transformations for unknown function and independent variable, and apply this results to the finding ofsolutions for several classes of integrable second order linear or inary epuations with variable coefficients and nonlinear equations.