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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Question

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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