四阶变系数微分方程化为常系数方程的一个充要条件

A Necessary and Sufficient Condition for Turning Four-order Differential Equation with Variable Coefficients into Constant Coefficient Equation

借助于自变量代换,在文献[1]的基础上,本文获得了四阶变系数线性微分方程y(4)+p(x)y'''+q(x)y″+r(x)y'+s(x)y=0化为四阶常系数方程的一个充分必要条件及若干推论。

On the basis of literature [ 1 ], by means of self-variable substitution, this paper obtains the sufficient and necessary condi- tion for turning four-order linear differential oquation with variable coefficients y^（4）＋p（x）y″＋q（x）y″＋r（xy）＇＋s（x）y=0 into four- order constant coefficient differential equation and some deductions.