You've got to juggle the two equations, multiply that by 4, multiply that by 3, add and subtract and so on.

同时处理这两个方程,这个两边乘以4,另一个两边乘以3,将两方程相加或相减求出答案

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

Everyone knows from calculus that if you're trying to find a function about which you know only the derivative, you can always add a constant to one person's answer without changing anything.

学过微积分的人都知道,如果你想根据已知的导数,求出其原函数,你总是可以给某人的答案,随便加一个常数,且不影响结果

耶鲁公开课 - 基础物理课程节选

Well, unfortunately, we know this is not the right answer, because if you take the first derivative, I get 2t.

遗憾的是,我们知道这还不是正确答案,因为如果对它求一阶导数,会得到2t

耶鲁公开课 - 基础物理课程节选