To determine The duration of time taken for the pollution concentration to decrease to the half of its original value. Explanation It is given that the rate of change in pollution equals the product of the flow rate and the pollution change and the model is defined as follows. y ′ = 175 ( p 4 − y 450 ) y ′ + 0.38 y = 175 ⋅ 0.0001 ( ∵ p = 0.04 % ) y ′ + 0.38 y = 0.0175 The above differential equation is of the form y ′ + p y = r , where p = 0.38 and r = 0.0175 . The general solution is given by, y ( x ) = e − h ( c + ∫ r e h d x ) ... ( 1 ) The integrating factor h is ∫ p d x and it is calculated as follows. ∫ p d x = 0.38 ∫ d x = 0.38 x Substitute the integrating factor h in equation (1) and obtain the general solution as follows. y ( t ) = e − 0

10th Edition

ISBN: 9781119455929

Author: Kreyszig

Publisher: WILEY

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Chapter 1.5, Problem 35P

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The duration of time taken for the pollution concentration to decrease to the half of its original value.

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Chapter 1.5, Problem 34P

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Chapter 1 Solutions

ADVANCED ENGINEERING MATHEMATICS (LL)

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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