DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

3rd Edition

ISBN: 9781119764564

Author: BRANNAN

Publisher: WILEY

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Textbook Question

Chapter 6.6, Problem 12P

The equations presented in Section 6.1 for modelling lead uptake, subsequent exchange between tissue compartments, and removal from the human body are

$x 1 ' = ( L + k 12 x 2 + k 13 x 3 ) − ( k 21 + k 31 + k 01 ) x 1 x 2 ' = k 21 x 1 − ( k 02 + k 12 ) x 2 x 3 ' = k 31 x 1 − k 13 x 3 .$

Employing the methods of Section 6.6, find the solution of this system subject to the initial conditions $x 1 ( 0 ) = 0 , x 2 ( 0 ) = 0$ and $x 3 ( 0 ) = 0$ using the parameter values $k 21 = 0.011 , k 12 = 0.012 , k 31 = 0.0039 , k 13 = 0.000035 , k 01 = 0.021 , k 02 = 0.016$ , and input function

$L ( t ) = { 35 , 0 ≤ t ≤ 365 , 0 , t > 365.$

Solve the problem in two stages, the first over the time interval $0 ≤ t ≤ 365$ and the second over the time interval $t ≥ 365$ . Evaluate the solution for the first stage at $t = 365$ to provide initial conditions for the second stage of the problem. You may wish to use a computer to assist your calculations. Check your results by comparing graphs of the solutions with the graphs in Figure $6.1.4$ or by comparing with an approximation obtained by using an initial value problem solver.

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Chapter 6.6, Problem 11P

Chapter 6.6, Problem 13P

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Chapter 6 Solutions

DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

Ch. 6.1 - If and Find : Ch. 6.1 - Verify that x=et(684)+2e2t(011) satisfies...Ch. 6.1 - Verify that =(ete2te3t4ete2t2e3tete2te3t)...Ch. 6.1 - In each of Problems through, transform equation...Ch. 6.1 - In each of Problems 4 through 9, transform...Ch. 6.1 - In each of Problems through, transform equation...Ch. 6.1 - In each of Problems through, transform equation...Ch. 6.1 - In each of Problems 4 through 9, transform...Ch. 6.1 - In each of Problems 4 through 9, transform...Ch. 6.1 - Derive the differential equationsfor x1(t) and...

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