The temperature of an object at time t is governed by the linear differential equation

Chapter 1, Problem 52

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The temperature of an object at time t is governed by the linear differential equation dT dt = k(T 5 cos 2t). At t = 0, the temperature of the object is 0F and is, at that time, increasing at a rate of 5F/min. (a) Determine the value of the constant k. (b) Determine the temperature of the object at time t. (c) Describe the behavior of the temperature of the object for large values of t.

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