As you’re starting to do the exercises in Chapter 2, here are some materials from across the web that might help you absorb these concepts and techniques.  Some of these I’ve already posted to the Discussion Forum, but thought it might be helpful to list them here again:

• The slides accompanying Chapter 2 of the textbook can be found here (pdf). Read slides 1-24 for a review of Sections 2.1 (linear FO equations) and 2.2 (separable FO equations)
• A nice set of notes from a Virginia Tech course on differential equations can be found here. For now, look at the pdfs titled “Solving First Order Linear Equations” (in particular the subsection on integrating factors) and “First Order Non-Linear Equations” (in particular the subsections on separable equations). Those subsections have a number of worked examples.  You could also back and read the first pdf in that set, titled “Introduction to Differential Equations” to review the basic concepts from Chapter 1.
• Khan Academy has a couple videos on separable equations and a couple more on integrating factors.  There’s also a couple on homogeneous equations, which are the topic of the last set of homework exercises from Sec 2.2
• Finally, I wrote up a 1-page summary of the method of integrating factors (from Sec 2.1), which you can find here.