The differential equation below models the temperature of a 94°C cup of coffee room, where it is known that the coffee cools at a rate of 1°C per minute when temperature is 74°C. Solve the differential equation to find an expression for th temperature of the coffee at time t. (Let y be the temperature of the cup of cof and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 94°C.) dy 1 dt 50 - 24) We now have Inly- 24| = -t+ C.and so ly- 24 = 50 Step 5 Consequently, we write y-K +24, where K-tec Step 6 Finally, using y (0) -94 allows us to solve for K- Step 7 The temperature of the coffee at the time is described by the following equation.

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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.