Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the dT body. That is, = K[M(t) – T(t), where K is a constant. Let K =0.04 (min) and the temperature of the medium be constant, M(t) = 290 kelvins. If the body is initially at 361 kelvins, use dt Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is kelvins. (Round to two decimal places as needed.)

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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.