利用齐次化原理求解常系数非齐次线性方程初值问题

Solving the Initial Value Problem of Non-homogeneous Linear Differential Equation with Constant Coefficients by Using Duhamel Principle

文章给出利用齐次化原理求解n阶常系数非齐次线性方程初值问题的方法.通过基本问题可得到原方程的解,避免了利用常数变易法求解的诸多不便,同时也将非齐次项的形式拓展到了所有可积函数.

We solve the initial value problem of non-homogeneous linear differential equation by using Duhamel principle. The solution can be obtained through the basic problem, so that we get over the inconvenience of variation of constants, meanwhile the inhomogeneous term can be expanded to all integrable functions.