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The Noyes-Whitney equation for the dynamics of the drug concentration is$$\frac{d c}{d t}=k\left(c_{s}-c\right)$$where $k$ and $c_{s}$ 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 $c=c_{s}\left(1-e^{-k t}\right)$ is the solution to this equation for the initial condition $c(0)=0 .$

The solution given satisfies the differential equation. Also, the differentialequation is an autonomous equation. For the detailed work, see the solution.

Calculus 2 / BC

Chapter 7

Differential Equations

Section 1

Modeling with Differential Equations

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

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Noyes-Whitney drug dissolu…

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Differential equations hav…

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arrested. The differential equation says of the concentration of drug during dissolution in pieces that see pieces of seas below C s. Since multiplication of two positive numbers is positive on Indy pieces is, if sees above sea essence multiplication of one positive number one native numbers native. We can verify this as follows. So substituting the function into the left hand side of the differential equation so we can write our left hand side as DC DT, which is equal to C S. C s tens que eat the power of negative. Katie, I know it's attracting K. C s. We could rewrite this that this is equal to a que si es minus K. C. S one Maya's eat the power of negative, Katie. So since C is equal to C s hands, one each apartment Katie here, that this is K. C s minus Casey, which is K. C s might see, and this is equal to the right hand side. So since the left hand side is equal to the right hand side, we have verified the solution

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