In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical solution is the correct one, and leads to an explanation of why the student solution is flawed. He suggests that this problem, or variations of it, can be used as an exercise for students familiar with basic integration techniques and numerical methods for differential equations. In particular, it reinforces to students that exact solutions need to be checked carefully, and how numerical solutions can reveal and highlight features of an exact solution. (Contains 2 figures.)