Suppose a raindrop evaporates as it falls but maintains its spherical shape. Assume that the rate at which the raindrop evaporates (that is, the rate at which it loses mass) is proportional to its surface area, where the constant of proportionality is –0.01. The density (mass per volume) of water at 3.98°C is 1 g/cm3. The surface area of a sphere is 4πr2, and its volume is 4πr3/3, where r is the radius. Assume no air resistance. (Project 8 models the motion of this raindrop under the influence of air resistance.) Assume that the initial radius is 0.3 cm. Determine the raindrop’s initial mass. Write a differential equation for the rate of change of mass as a function of r. Write an equation for r as a function of mass

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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.