一类高阶常系数线性微分方程的特解公式  

The Formula of Special Solution for a Kind of High-order Linear Differential Equation with Constant Coefficients

作　　者：张守贵[1] 

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《四川理工学院学报（自然科学版）》2016年第3期93-95,共3页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11471063)

摘　　要：高阶微分方程是常微分方程和高等数学的重要内容,但是现有的方法比较难掌握。对一类常见的高阶非齐次常系数线性常微分方程得到了求其特解的一般公式。首先引入了有关两个函数乘积高阶导数的莱布尼兹公式和一个组合数性质,然后利用待定系数法得到了求解该方程特解的一般公式。并给出了详细的证明过程和若干具体算例。结果表明:该方法的公式推导过程非常简单,所得公式有较高的实用性和有效性。High-order differential equation is an important content in courses of ordinary differential equation and advanced mathematics,but existing methods are difficult to be mastered. For a kind of n-order linear and non-homogeneous ordinary differential equation with constant coefficients,the general formula of the special solutions is presented in this paper.The Leibniz formula for higher order derivatives of product of two functions and a property for the number of combinations are first introduced,and the general formula of the special solutions for the equation is obtained by method of undetermined coefficients. The process of proofs and some examples are also given in detail. The results show the formula is very simple and illustrate the effectiveness and practicality of the method presented.

关 键 词：n阶线性常微分方程 特解公式 待定系数法 莱布尼兹公式 

分 类 号：O175.1[理学—数学]