高阶常系数线性非齐次微分方程几种解法

Higher order linear non-homogeneous differential equation solving methods

关于高阶常系数非齐次线性微分方程特解的求法,国内的《常微分方程》教材大多采用待定系数法进行求解,当方程的阶数较高时此方法较为繁琐。文章除了介绍高阶方程的待定系数法外,还介绍了常数变易法、拉普拉斯变换法、微分算子法,分析了各种解法的优缺点及适合的方程类型.

As to the solution of higher order constant coefficient non - homogeneous linear differential equation, domestic teaching ＂Ordinary Differential Equations＂ used to solve it with undetermined coefficient method. When the order of the equation is higher, this method is more complicated. Besides introducing the undetermined coefficient method for order equation, but also introduced the constant variation method, Laplace transform method, the differ- ential operator method, and analyzed the advantages and disadvantages of various solution of the equation as well as the types of proper equation.