Find the function satisfying the differential equation f'(t) = f(t) = 2t and the condition f(3) = 9. f(t) =

Find the particular solution of the differential equation that satisfies the initial condition. f'(x) - 6x, f(0) = 3 (x)

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes

Verify that the function is a solution of the differential equation on some interval, for any choice of the arbitrary constants appearing in the function.