应用发散级数求常系数线性非齐次常微分方程特解的注记
Note on the Application of Divergent Series for Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients
摘要：
求解常系数非齐次线性常微分方程的特解有许多方法。通常已知的有待定系数待定系数法、拉普拉斯变换法和微分算子法。后一种方法有时使用逆微分算子的麦克劳林展开，但仅在所得到的级数收敛的情况下。本文还讨论了如果无穷级数是发散的，如何仅利用级数的项和发散级数的求和方法求出其特解。
英文摘要：
There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coefficients, Laplace transform method and differential operator method are generally known. The latter mentioned method sometimes uses the Maclaurin expansion of an inverse differential operator but only in the case when the obtained series is convergent. The present work deals also with how to find a particular solution if the corresponding infinite series is divergent, using only the terms of that series and the method of summation of divergent series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
