二阶变系数线性微分方程的几个可积类型

Some integrable classes of the second order linear ordinary differential equations with variable coefficients

文[1]给出了一些变系数线性微分方程的可积类型,[2、3]利用“连锁”法也给出了一些变系数线性微分方程的可积类型,且包含了[1]的结果.

In this paper,some conditions of reducing the second order linear ordinarydifferential equations with variable coefficients to those with constant coefficients are given,by means of the transformations for unknown function and independent variable,and applythis results to the finding of solutions for several classes of integrable second order linearordinary equations with variable coefficients and nonlinear equations.