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dx = -.5x + 2y dt dy = .4x - 4y dt Solve for x(t) and y(t) given the initial conditions stated above. Simplify each expression as much as possible and write them in the blanks below. V/+1

dx = -.5x + 2y dt dy = .4x - 4y dt Solve for x(t) and y(t) given the initial conditions stated above. Simplify each expression as much as possible and write them in the blanks below. V/+1

Advanced Engineering Mathematics
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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A patient initially has a concentration of 50mg/L of morphine in her blood and 70mg/L in her cerebrospinal fluid. Suppose that the drug moves into the cerebrospinal fluid at a per-capita rate of .4 and that the amount that is moved back from the cerebrospinal fluid to the bloodstream is .2. Suppose further that the metabolism of medicine in the bloodstream is .1 and the metabolism of the drug in the cerebrospinal fluid is .2 Blood cerebrospinal fluid ( brain ) Let x(t) represent the concentration in the blood and y(t) represent the concentration in the brain area. Finish this compartment diagram . Explain why this is a mathematical model for this process. dx = -.5x + .2y dt dy 3 4х — .4у dt Solve for x(t) and y(t) given the initial conditions stated above. Simplify each expression as much as possible and write them in the blanks below. X(t)=. Y(t)=
Transcribed Image Text:A patient initially has a concentration of 50mg/L of morphine in her blood and 70mg/L in her cerebrospinal fluid. Suppose that the drug moves into the cerebrospinal fluid at a per-capita rate of .4 and that the amount that is moved back from the cerebrospinal fluid to the bloodstream is .2. Suppose further that the metabolism of medicine in the bloodstream is .1 and the metabolism of the drug in the cerebrospinal fluid is .2 Blood cerebrospinal fluid ( brain ) Let x(t) represent the concentration in the blood and y(t) represent the concentration in the brain area. Finish this compartment diagram . Explain why this is a mathematical model for this process. dx = -.5x + .2y dt dy 3 4х — .4у dt Solve for x(t) and y(t) given the initial conditions stated above. Simplify each expression as much as possible and write them in the blanks below. X(t)=. Y(t)=
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