​Newton's Law of Cooling says that the rate at which a body cools is proportional to the difference C in temperature between the body and the environment around it. The temperature​ f(t) of the body at time t in hours after being introduced into an environment having constant temperature T0 is f(t)=T0+C e −kt​, where C and k are constants.   A cup of coffee with temperature 130°F is placed in a freezer with temperature 0°F. After 5 minutes, the temperature of the coffee is 87°F. Use​ Newton's Law of Cooling to find the​ coffee's temperature after 10 minutes.

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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.