一类二阶常系数非齐次线性微分方程及边值问题的解法

The Solution of a Particular 2^(nd)-order Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients and Boundary Value Problem

利用非齐次方程通解方法和Green函数法给出了非齐次项为点源函数的二阶常系数线性常微分方程及边值问题的求解方法和公式.然后以渗流力学一类具体问题为例进行了论证.结果表明这两种方法在本质上是一致的,所得到的结果是相互吻合的.该点源解可用于分析相关边值问题,并可用来求解具有一般非齐次项的微分方程及相关定解问题.

Utilizing methods of general solution and Green＇s function, the solution of a 2nd-order linear ordinary differential equation （ODE） and the corresponding boundary value problem with a nonhomogeneous term in the form of point source function is presented. Then it is validated by a practical problem in the field of porous media flow. It indicates that the above two methods are consistent with each other in essence. The presented solution is of great use to analyze the relevant boundary value problems. Moreover, the methods in this paper can be applied to solve the linear ODE and the related definite problems with a general nonhomogeneous term.