高阶变系数线性微分方程的一些新的可积类型

Some New Integrable Types of Higher Order Linear Ordinary Differential Equations with Variable Coefficients

借助双变换—未知函数的变换和自变量的变换,将几类高阶变系数线性微分方程化为相应的常系数线性微分方程,从而顺利求得它们的通解,得到了变系数线性微分方程新的可积类型,所得结果极大地推广了著名的Euler方程及前人的一些的工作,并给出了相应的实例加以佐证.

By means of double transformation--linear transformation of unknown function and self-variable transformation, several classes of higher order linear differential equations with variable coefficients are turned into linear differential equations with constant coefficients. Thus, general solutions of equations mentioned above can be obtained, meanwhile, the famous Euler equations and some predecessorls results on this issue are expanded.