**Get inspired:**

On October 14, 2012, Felix Baumgartner skydived from a heigh of 39 km (24 mi), reaching an estimated speed of 1,342 km/hr (834 mph). He descended in free-fall for 4 minutes and 20 seconds. You can watch the footage, which is impressive and scary all at once. At about 2:30 into the video, he starts getting out of his capsule. The camera shot at 3:00 is terrifying. He jumps at 3:34. He deploys his parachute at 7:55. He lands at 12:37. What does this have to do with differential equations? Falling objects are one of the most fundamental problems modeled with first order differential equations.

**By the end of this lesson, you should be able to:**

- Determine the order of a given differential equation.
- Check if a given function is a solution to a differential equation.
- Explain the difference between a general solution and a particular solution.
- Interpret a first order differential equation as a slope field.
- Solve first order differential equations via separation of variables (when it is possible).
- Determine whether a given first order linear differential equation is homogeneous or inhomogeneous.
- Solve linear first order differential equations via integrating factors (when it is possible).

**Before class:**

- Read Polking, Boggess and Arnold, Sections 2.1 - 2.4.
- Watch pencasts (linked above).
- Check yourself before you wreck yourself.

**In class, we will:**

- Demonstrate DFIELD software for plotting direction fields.
- Work on this activity (key).

**After class, please:**

- Do these problems.