Program Explanation Given information: The pollutant concentration is c ( t ) = 10 L / m 3 , average depth of water is 2 meters the liquid pollutant flows at the rate of 2 × 10 5 m 3 per month. Explanation: The mount of solute x ( t ) satisfies the below differential equation. d x d t = r i c i − r o V x ....... (1) Here, r i , c i , r o are constants and V is the volume of the solution. The value of r i in millions of liters per second is calculated as, r i = 200 × 10 3 m 3 / month = 0.2 × 10 6 m 3 / month = 1 5 million liters The rate of inflow and outflow is same, so r o = 1 5 and the value of volume in millions of cubic meters is 2 . Substitute 1 5 , r i and 1 5 for r o , 10 for c i and 2 for V in equation (1). d x d t = 1 5 ⋅ 10 − 1 5 2 x d x d t = 2 − 1 10 x d x d t + 1 10 x = 2 The above equation is a linear first-order equation and its solution is calculated as, x e 1 10 ∫ d t = 2 ∫ e 1 10 ∫ d t d t x e t 10 = 2 ∫ e t 10 d t = 2 1 10 e t 10 + C = 20 e t 10 + C Simplify the above equation. x = 20 + C e − t 10

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 1.5, Problem 45P

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Program Description: Purpose of problem is to calculate the amount of pollutant x(t) and show that the graph is common with the steadily rising curve and the time taken pollutant to reach 10L/m3 .

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Chapter 1.5, Problem 44P

Chapter 1.5, Problem 46P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - 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Prob. 40P Ch. 1.5 - Prob. 41P Ch. 1.5 - Prob. 42P Ch. 1.5 - Figure 1.5.7 shows a slope field and typical...Ch. 1.5 - Prob. 44P Ch. 1.5 - Prob. 45P Ch. 1.5 - Prob. 46P Ch. 1.6 - Prob. 1P Ch. 1.6 - Prob. 2P Ch. 1.6 - Prob. 3P Ch. 1.6 - Prob. 4P Ch. 1.6 - Prob. 5P Ch. 1.6 - Prob. 6P Ch. 1.6 - Prob. 7P Ch. 1.6 - Prob. 8P Ch. 1.6 - Prob. 9P Ch. 1.6 - Prob. 10P Ch. 1.6 - Prob. 11P Ch. 1.6 - Prob. 12P Ch. 1.6 - Prob. 13P Ch. 1.6 - Prob. 14P Ch. 1.6 - Prob. 15P Ch. 1.6 - Prob. 16P Ch. 1.6 - Prob. 17P Ch. 1.6 - Prob. 18P Ch. 1.6 - Prob. 19P Ch. 1.6 - Prob. 20P Ch. 1.6 - Prob. 21P Ch. 1.6 - Prob. 22P Ch. 1.6 - Prob. 23P Ch. 1.6 - Prob. 24P Ch. 1.6 - Prob. 25P Ch. 1.6 - Prob. 26P Ch. 1.6 - Prob. 27P Ch. 1.6 - Prob. 28P Ch. 1.6 - Prob. 29P Ch. 1.6 - Prob. 30P Ch. 1.6 - Prob. 31P Ch. 1.6 - Prob. 32P Ch. 1.6 - Prob. 33P Ch. 1.6 - Prob. 34P Ch. 1.6 - Prob. 35P Ch. 1.6 - Prob. 36P Ch. 1.6 - Prob. 37P Ch. 1.6 - Prob. 38P Ch. 1.6 - Prob. 39P Ch. 1.6 - Prob. 40P Ch. 1.6 - Prob. 41P Ch. 1.6 - Prob. 42P Ch. 1.6 - 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Program Description: Purpose of problem is to calculate the amount of pollutant x ( t ) and show that the graph is common with the steadily rising curve and the time taken pollutant to reach 10 L / m 3 .

Solution Summary: The author calculates the amount of pollutant x(t) and shows that the graph is common with the steadily rising curve.

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Program Description: Purpose of problem is to calculate the amount of pollutant x(t) and show that the graph is common with the steadily rising curve and the time taken pollutant to reach 10L/m3 .

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Chapter 1 Solutions