二阶变系数线性微分方程及其衍生方程

Second-order Variation Coefficient Linear Differential Equation and Its Derivative Equation

目的探究二阶变系数线性微分方程的求解.方法从构造二阶变系数线性微分方程解的形式出发,给出正负各级衍生方程的概念.结果得到二阶线性微分方程衍生方程的存在性,各级衍生方程的递推公式,导出二阶变系数线性微分方程与衍生方程解的关系.结论得到二阶变系数线性微分方程求解方法的重要结论.

Objective To explore the solution to second-order variation coefficient linear differential equations.Methods By constructing the models of the solution to this kind of equation,the concept of all levels of derivative equations is obtained.Results The existence of the derivative equations,and the recurrence formula of those equations are obtained,and the relations between the primitive equation and the derivate equations are deduced.Conclusion Important conclusions of the solution to this kind of equations are obtained.