The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.

解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件

耶鲁公开课 - 基础物理课程节选