Consider a pond that initially contains 10 million gal of fresh water. Stream 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 through an overflow culvert at the same rate. The concentration y(t) of the incoming water varies periodically with time t, measure in years, according to the expression y(t) = 2+ sin 2t g/gal. a. Write out the differential equation that models this scenario. Include the initial value as well. b. Solve the initial value problem from a. You may use technology to help with the integration. c. Plot this solution for t e (0,20) years. What is happening to this pond as time moves on?
Consider a pond that initially contains 10 million gal of fresh water. Stream 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 through an overflow culvert at the same rate. The concentration y(t) of the incoming water varies periodically with time t, measure in years, according to the expression y(t) = 2+ sin 2t g/gal. a. Write out the differential equation that models this scenario. Include the initial value as well. b. Solve the initial value problem from a. You may use technology to help with the integration. c. Plot this solution for t e (0,20) years. What is happening to this pond as time moves on?
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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Transcribed Image Text:1. Consider a pond that initially contains 10 million gal of fresh water. Stream 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 through an overflow culvert at the same rate. The
concentration y(t) of the incoming water varies periodically with time t, measure in
years, according to the expression y(t) = 2 + sin 2t g/gal.
%3D
a. Write out the differential equation that models this scenario. Include the initial value
as well.
b. Solve the initial value problem from a. You may use technology to help with the
integration.
c. Plot this solution for t e (0,20) years. What is happening to this pond as time moves
on?
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