Consider a pond that initially contains 10 million gal of fresh water. Water containing an undesirable chemical flows into the pond at the rate of 5 million gal/yr, and the mixture in the pond flows out at the same rate. The concentration y(t) of chemical in the incoming water varies periodically with time according to the expression y(t) = 2 + sin 2t g/gal. Construct a mathematical model of this flow process and determine the amount of chemical in the pond at any time.
Consider a pond that initially contains 10 million gal of fresh water. Water containing an undesirable chemical flows into the pond at the rate of 5 million gal/yr, and the mixture in the pond flows out at the same rate. The concentration y(t) of chemical in the incoming water varies periodically with time according to the expression y(t) = 2 + sin 2t g/gal. Construct a mathematical model of this flow process and determine the amount of chemical in the pond at any time.
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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Consider a pond that initially contains 10 million gal of fresh water. Water containing an
undesirable chemical flows into the pond at the rate of 5 million gal/yr, and the mixture in the pond flows out at the same rate. The concentration y(t) of chemical in the incoming water varies periodically with time according to the expression y(t) = 2 + sin 2t g/gal. Construct a mathematical model of this flow process and determine the amount of chemical in the pond at any time.
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