1315 Drug dissolution Differential equations have been used extensively in the study of

Chapter 7, Problem 13

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1315 Drug dissolution Differential equations have been used extensively in the study of drug dissolution for patients given oral medications. The three simplest equations used are the zero-order kinetic equation, the Noyes-Whitney equation, and the Weibull equation. All assume that the initial concentration is zero but make different assumptions about how the concentration increases over time during the dissolution of the medication. 13. The zero-order kinetic equation states that the rate of change in the concentration of drug c (in mgymL) during dissolution is governed by the differential equation dc dt k where k is a positive constant. Is this differential equation pure-time, autonomous, or nonautonomous? State in words what this differential equation says about how drug dissolution occurs. What is the solution of this differential equation with the initial condition cs0d 0? 14. The Noyes-Whitney equation for the dynamics of the drug concentration is dc dt kscs 2 cd where k and cs are positive constants. Is this differential equation pure-time, autonomous, or nonautonomous? State in words what this differential equation says about how drug dissolution occurs. Verify that c css1 2 e2ktd is the solution to this equation for the initial condition cs0d 0. 15. The Weibull equation for the dynamics of the drug concentration is dc dt k t b scs 2 cd where k, cs, and b are positive constants and b , 1. Notice that this differential equation is undefined when t 0. Is this differential equation pure-time, autonomous, or nonautonomous? State in words what this differential equation says about how drug dissolution occurs. Verify that c cs(1 2 e2t 12b ) is a solution for t 0, where kys1 2 bd.