Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object an the temperature of its surroundings. (a) Based on this physical principle, derive a differential equation of the form dT dt = f(V) for the temperature of the object at any time. All constants of proportionality should be positive.

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A: We can solve this problem as follows:

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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.