The bookstore is selling Zill's textbook, 10th edition. However, you are not required to buy this book. Any edition of Zill will do. In fact, any textbook on differential equations written in the last thirty years will cover the same topics (perhaps with different notation, but you should be capable of adjusting for that). I do strongly suggest that you obtain a textbook, study it, and keep it for future reference.
If you use another text, you should be able to find appropriate readings by matching the lecture topic to your text's table of contents or index, with the following hints