Chapter 26 Integrating Differential Equations using Laplace Transforms

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Finger Print Method - Example 3

The differential equation for amount of drug in body according to the two compartment model after an IV bolus (Dose) can be written as:

Equation 26.8.1 Laplace Transform of Amount in the Body after an IV Bolus - Two Compartment model

Note that the denominator has a power of 2 in s and no repeating terms. The numerator has a power of 1 in s. Therefore the fingerprint method can be applied.

Setting the denominator to zero:

(s + α) * (s + β) = 0

gives the two roots -α and -β.

The finger print method can then be applied as illustrated in the video below.

Figure 26.8.1 Video illustrating the Finger Print Method - 3

The solution

Equation 26.8.2 Integrated Equation for Amount in the Body after an IV Bolus - Two Compartment

Dividing both sides by V₁ provides the more familiar values A and B in the equation for Cp versus time. A and B were defined earlier in Equation 19.2.4.

Equation 26.8.3 Integrated Equation for Amount in the Body after an IV Bolus - Two Compartment

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Pharmacy Math Part Two
A selection of Pharmacy Math Problems