Consider a 46∘F object placed in 64∘F room. (a) Write a differential equation for H, the temperature of the object at time t, using k>0 for the constant of proportionality, and write your equation in terms of H, k, and t. H′=  (b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant C, which appears as the coefficient of an exponential term, and the growth factor k. H=  (Your answer may involve the constant of proportionality k.) (c) The temperature of the object is 46∘F initially, and 52∘F one hour later. Find the temperature of the object after 3 hours. H(3)=  (In Degrees F)

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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.