If you don't have the units, then if you say the answer is 19, then we don't know what it means.

如果没有的话,比如你的答案是十九,那我们就不知道这是什么意思

耶鲁公开课 - 基础物理课程节选

But then having found one answer, you can add to it anything that gets killed by the act of taking derivatives.

一旦你算出了一个答案,你就可以往式子里加入任何,在求完导后消失的项

耶鲁公开课 - 基础物理课程节选

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

Conversely, if you get an answer and it doesn't seem to make sense, then you've got to go back and ask, am I violating some of the assumptions, and here you will find the assumption that the particle had that acceleration a is true as long it's freely falling under gravity but not when you hit the ground.

反过来说,如果你得到一个结果,发现似乎是错的,那么你就应该回过头来问问自己,我是不是违反某些前提了,这个模型中,你就发现,只要质点在重力作用下自由下落,质点具有加速度a的前提是正确的,但是落地后就不成立了

耶鲁公开课 - 基础物理课程节选