You've seen a few examples of applications of DE's in the homework but not any where you take a problem from the beginning of setting up a DE based on a description of the situation. As an example of that, let's look at free fall WITH air resistance.
When learning about projectile motion and free-fall in Introductory Physics, you start with the assumption that the object is in a vacuum. This helps to illustrate the fundamental principles but it isn't very satisfying since air resistance is obviously a HUGE factor in the real world.
Here are some notes and a video that will walk you through understanding the dynamics of free fall when air resistance is taken into account.
Video
Next, at the very beginning of this chapter, I had you watch a video and do some practice problems on Khan Academy that involved translating rate and proportionality statements into DE's.
I'd like you to revisit that and go a bit more in depth with modeling some important real world situations.
Applications of DE's: