The secretion of hormones into the blood is often a periodic activity. If a horm

Question

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 of the level of the hormone in the blood may be represented by the initial value problem dx/dt=-alpha-beta cos(pit/12)-k x,x(0)=x0 where x(t) is the amount of hormone in the blood at time t, alpha is the average secretion rate, beta is the amount of daily variation in secretion, and k is a positive constant reflecting the rate at which the body removes the hormone from the blood. If alpha = beta = 1, k = 2 and x0 = 10, solve for x(f).

Explanation / Answer

dx/dt = 1 - cos(t/12) - 2x

x(0) = 10

10 = c1 + 2 /2(2 + 576)

c1 = {5760 +192 }/2(2 + 576)

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