The Noyes-Whitney equation for the dynamics of the drug concentration is dc/dt = k(cs - c) where k > 0 and cs > 0 are constants. Solve the initial-value problem for the Noyes-Whitney drug dissolution equation. (Let c(0) = c0.) c(t) =
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We are given the Noyes-Whitney equation for the dynamics of drug concentration: $$ \frac{dc}{dt} = k(cs - c) $$ where $k > 0$ and $cs$ are constants. Show more…
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13-15 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. The zero-order kinetic equation states that the rate of change in the concentration of drug $c($ in $\mathrm{mg} / \mathrm{mL})$ during dissolution is governed by the differential equation $$\frac{d c}{d t}=k$$ 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 $c(0)=0 ?$
Differential Equations
Modeling with Differential Equations
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: $$ \frac{d c}{d t}=\frac{k}{t^{b}}\left(c_{s}-c\right) $$ where $k$ and $c_{s}$ are positive constants and $0<b<1$. Verify that $$ c(t)=c_{s}\left(1-e^{-a t^{1-b}}\right) $$ is a solution of the Weibull equation for $t>0$, where $\alpha=k /(1-b) .$ What does the differential equation say about how drug dissolution occurs?
Sri K.
Let C(t) be the concentration of drug in the bloodstream. As the body eliminates the drug, C(t) decreases at a rate that is proportional to the amount of the drug that is present at the time. Thus, C'(t) = -kC(t), where k is a positive number called the elimination constant of the drug. a) If C(0) = 70 mg/litre (the concentration at time t = 0), find C(t), the concentration at time t, by solving the differential equation. (5 marks) Note: You must include how to solve this DE as part of your solution.
Vishal P.
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