Chapter 9.1, Problem 29E

Differential equations have been used extensively in the study of drug dissolution for patients given oral medications. One such equation is the Weibull equation for the concentration c(t) of the drug:

$\frac{dc}{dt}=\frac{k}{t^b}(c_s-c)$

where k and c_s are positive constants and 0 < b < 1. Verify that

$c(t)=c_s(1-e^{-\alpha t^{1-b}})$

is a solution of the Weibull equation for t > 0, where α = k/(1 − b). What does the differential equation say about how drug dissolution occurs?