V. A mixing problem in medicine: A patient is given morphine intra- venously at the rate of r milligrams per hour. (The constant r is unspecified for now.) Morphine is absorbed from the bloodstream of the patient at a rate equal to 34.7% of the amount in the bloodstream per hour. (a) Let A(t) be the amount of morphine, in mg, in the patient's blood- stream aftert hours. Find a differential equation for A(t). (b) Find any equilibrium solutions of the differential equation. (c) Initially, there is no morphine in the patient's bloodstream. Find the solution of the differential equation that satisfies the appropriate initial condition.
V. A mixing problem in medicine: A patient is given morphine intra- venously at the rate of r milligrams per hour. (The constant r is unspecified for now.) Morphine is absorbed from the bloodstream of the patient at a rate equal to 34.7% of the amount in the bloodstream per hour. (a) Let A(t) be the amount of morphine, in mg, in the patient's blood- stream aftert hours. Find a differential equation for A(t). (b) Find any equilibrium solutions of the differential equation. (c) Initially, there is no morphine in the patient's bloodstream. Find the solution of the differential equation that satisfies the appropriate initial condition.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please help, using basic calculus rules
Transcribed Image Text:V. A mixing problem in medicine: A patient is given morphine intra-
venously at the rate of r milligrams per hour. (The constant r is unspecified
for now.) Morphine is absorbed from the bloodstream of the patient at a rate
equal to 34.7% of the amount in the bloodstream per hour.
(a) Let A(t) be the amount of morphine, in mg, in the patient's blood-
stream aftert hours. Find a differential equation for A(t).
(b) Find any equilibrium solutions of the differential equation.
(c) Initially, there is no morphine in the patient's bloodstream. Find
the solution of the differential equation that satisfies the appropriate initial
condition.
(d) What happens to A(t) after a long time? Justify your answer.
(e) At what rate r should the patient be given morphine intravenously so
that the amount of morphine in the bloodstream approaches 8.0 milligrams?
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