二阶变系数线性微分方程化为标准型的求解

Solution of Two Order Variable Coefficient Linear Differential Equation into Standard Form

摘要: 本文给出关于二阶变系数线性微分方程的求解，转变以往降阶的常规思维，利用其标准型进行求解。在标准型的求解中，通过对原微分方程的化简，利用余函数和特积分，分别求出其标准型齐次和非齐次的解，最后构造出原方程通解。

Abstract: This paper discusses the solution of the two order variable coefficient linear differential equation with standard type, which transforms the traditional method of reducing order. Through simpli-fying the original differential equation and using means of cofunction and particular integral, we can get the homogeneous and non-homogeneous solution of the standard type. Finally we can construct the general solution of the original equation.