%0 Journal Article
%T 一种基于刘维尔公式的二阶非齐次线性微分方程的解法<br>A Solution Method for Second-Order Non-Homogeneous Linear Differential Equations Based on Liouville&#8217;s Formula
%A 朱永婷
%A 张光威
%J Pure Mathematics
%P 281-285
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.154131
%X 已知二阶齐次线性微分方程一个非零特解的情况下&#65292;利用常数变易法&#65292;在刘维尔公式的基础上&#65292;给出求解二阶非齐次线性微分方程通解的方法和一般公式&#65292;并附以两个例题验证该方法在求解此类微分方程的有效性&#65292;这对学习和研究高阶线性微分方程具有借鉴和启迪意义。<br>Given a non-zero particular solution of a second-order homogeneous linear differential equation, by using the method of variation of constants and based on Liouville&#8217;s formula, this paper presents the method and general formula for finding the general solution of second-order non-homogeneous linear differential equations. Two examples are attached to verify the effectiveness of this method in solving such differential equations, which has reference and enlightenment significance for the study and research of higher-order linear differential equations.
%K 刘维尔公式&#65292
%K 二阶线性微分方程&#65292
%K 常数变易法<br>Liouville&#8217
%K s Formula
%K Second-Order Linear Differential Equation
%K Variation of Constants Method
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=112395