SIAM Review, Volume 66, Issue 1, Page 149-160, February 2024.
In a recent article in this journal, Gouveia and Stone [``Generating Resonant and Repeated Root Solutions to Ordinary Differential Equations Using Perturbation Methods,” SIAM Rev., 64 (2022), pp. 485--499] described a method for finding exact solutions to resonantly forced linear ordinary differential equations, and for finding the general solution of repeated root linear systems. It is shown here that applying their mathematical justification directly yields a method that is faster and algebraically simpler than the method they described. This method seems to be unknown in the undergraduate textbook literature, although it certainly should be present there as it is elegant and simple to apply, generally giving solutions with much less work than variation of parameters.

中文翻译：

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共振强迫常微分方程和重根

SIAM Review，第 66 卷，第 1 期，第 149-160 页，2024 年 2 月。
在本杂志最近的一篇文章中，Gouveia 和 Stone [“使用扰动方法生成常微分方程的共振和重复根解”，SIAM Rev.， 64 (2022), pp. 485--499]描述了一种寻找共振强迫线性常微分方程的精确解以及寻找重复根线性系统的通解的方法。这里表明，直接应用他们的数学论证会产生一种比他们描述的方法更快、代数更简单的方法。这种方法在本科教科书文献中似乎是未知的，尽管它肯定应该存在，因为它优雅且易于应用，通常提供比参数变化更少的工作量的解决方案。