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Heres another example of the application of differential equations. You can imagine say someone who enjoys skydiving, jumping out of an airplane. Gravity is pulling him down, so hes under constant acceleration due to gravity, he keeps falling faster and faster. But you know that eventually his speed is going to stop increasing. Thats because of the air resistance pushing up on him as he falls. So, his final velocity as free-falling skydiver is going to approach some constant velocity. He will stop accelerating. So here, I want to see if we can derive the differential equation for that, and then solve the differential equation. So, we have a skydiver, maybe its best to draw some diagram here. So, we have some skydiver whos falling under gravity. We have to define some coordinate system. So, lets define the X-axis to be pointing up. So, the skydiver has forces on him. So, for the sake of this diagram, lets assume that his velocity is going to be down
