Explanation Given: Quantity of water in the tank is 500 gallons , quantity of salt per gallon of brine is 2 pounds and the rate at which brine is pumped into the tank is 5 gal / min . The mixed solution is pumped out at the same rate. Calculation: Calculate the rate of salt entering into the tank. R in = ( 2 lb gal ) ⋅ ( 5 gal min ) = 10 lb min Let A be the quantity of salt in the tank. Calculate the rate of outflow of salt. R out = ( A 500 lb gal ) ( 5 gal min ) = A 100 lb / min Consider the equation for the mixing of two fluids. d A d t = R i n − R o u t d A d t = 10 − A 100 d A d t + A 100 = 10 (1) Compare equation (1) with d A d t + p ( t ) A = Q ( t ) . The value of p ( t ) is 1 100 and Q ( t ) is 10 . Calculate the integrating factor. I F = e ∫ p ( t ) d t = e ∫ 1 100 d t = e t 100 Solve the differential equation using the integrating factor e t 100

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

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Chapter 2.7, Problem 23E

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Calculate the number of pounds of salt in the tank at time t.

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Chapter 2.7, Problem 22E

Chapter 2.7, Problem 24E

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