n阶常系数线性微分方程和n阶欧拉方程的积分因子解法  

The Integral Factor General Solution of the n-order Ordinary Coefficient of Linear Differential Equations and the n-order Euler's Equation

作　　者：宁荣健[1] 时军[1] NING Rong jian;SHI Jun(School of Mathematics, Hefei University of Technology, Hefei 230009, China)

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《大学数学》2017年第5期44-48,共5页College Mathematics

基　　金：安徽省重大教学改革项目(2015zdjy020);高等学校大学数学教学研究与发展中心项目(2015);唐烁名师工作室

摘　　要：通过引入n个积分因子,给出了n阶常系数线性微分方程y^(n)+p_1y^(n-1)+p_2y^(n-2)+…+p_(n-1)y′+p_ny=f(x)的积分因子解法,并进而得到n阶欧拉方程x^ny^(n)+p_1x^(n-1) y^(n-1)+…+p_(n-1)xy′+p_ny=f(x)的积分因子解法.该方法对任意的可积函数f(x),均可给出其通解形式,具有一定的理论研究价值和实际应用价值.By introducing a number of integral factors,we provide the integral factor general solution of the n order ordinary coefficient of linear differential equations y(n)+p1y(n-1)+p2y(n-2)+…+pn-1y′+pny=f(x).and then,we also provide the integral factor general solution of the n order Euler’s equationxny(n)+p1xn-1y(n-1)+…+pn-1xy′+pny=f(x).Using this method,we can get the formal general solution for any Integrable function f(x),so the method has certain theoretical research value and practical application value.

关 键 词：n阶常系数线性微分方程 n阶欧拉方程 积分因子 通解 

分 类 号：O13[理学—数学] O172.2[理学—基础数学]