A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a horizontal​ road) passes directly beneath it going 30 mi/hr (44 ft/s​). If the balloon rises vertically at a rate of 13 ft/s​ what is the rate of change of the distance between the motorcycle and the balloon 7 seconds later? Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon.  Write an equation relating x, y, and z. Answer the following question Find the rate of change of the distance between the motorcycle and the balloon after 7 seconds.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.