If you'd like something else to look at, you can check out M. Braun's Differential Equations and Their Applications . In problem 2, change the x's to t's. There will be two midterms. Here are answers to practice midterm 1. Here are answers to practice midterm 2.
References are to the text.
Recurrences, a discrete analogue of differential equations. Integrating factors for first-order linear ODEs. Existence and uniqueness of solutions in that case. Problems with differentials. The Brachistochrone problem.