一类二阶变系数非齐次线性微分方程的通解

General Solution of a Class of Second Order Nonhomogeneous Linear Differential Equations with Variable Coefficients

为了对形如y″+p(x)y′+q(x)y=f(x)的二阶变系数非齐次线性微分方程的通解进行研究,利用高阶微分方程的常数变易法,在齐次情形的基础上给出了非齐次情况下的通解公式,将结果推广至二阶欧拉方程,并举例说明了具体应用.

In order to study the general solution of the second-order nonhomogeneous linear differential e-quation with variable coefficients,such as y″+p(x)y′+q(x)y=f(x),this paper uses the constant variationmethod of the higher-order differential equation,on the basis of the homogeneous case,gives the general solutionformula of the nonhomogeneous case,extends the result to the second-order Euler equation,and gives examplesto illustrate the specific application.