Verifying the Solution of a Differential Equation

I have found that a lot of students get intimidated by the language of these problems, and that most students are surprised when they find out how truly easy it is to do these problems. When you are this far into an AP Calculus course, you just sort of expect the course to continue to up its level of difficulty on you. Then when you see very official sounding language like, “verify the solution of a differential equation”, you often think this has to be some complex process. I mean they are asking me to “verify” something.

The reality is that these problems usually only require some very straightforward derivative processes mixed with a little substitution of variables, and that is all.