A bottle of milk was taken from a refrigerator and put in a bowl of hot water to warm. According to Newton's empirical law of cooling, change of temperature of the milk in the bottle M(t) and change of temperature of water in the bowl W (t) can be described by the differential equations dM =-k (M – W) dt dW -k> (W - Ta)– k3 (W – M), dt where t is time (in minutes), Ta is the ambient temperature, k1 = 0.1, k2 and k3 0.03, = 0.18 are constants of proportionality. The temperatúre in the refrigerator is 5°C, the room temperature is 20°C and the initial temperature of the water in the bowl is 80°C. a) Find the temperature of milk and water as function of time. b) Find the values of W(t) and M(t) when t → .

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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.