Fundamentals of Differential Equations
Problem 37E: Secretion of Hormones.
The secretion of hormones into the blood is often a periodic activity. If a hormone is secreted on a 24-hour cycle, then the rate of change in the level of hormone in the blood may be represented by the initial value problem:
where x(t) is the amount of hormone in the blood at time t, α is the average secretion rate, β is the amount of daily variation in the secretion, and k is a positive constant reflecting the rate at which the body removes hormones from the blood. If α = β = 1, k = 2, and x0 = 10, solve for x(t).
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