A 94 gallon tank is half full of water and 9 pounds of is pumping water with a concentration 6 pounds of sugar per gallon into this tank at a rate of 4 gallons per minute. A second pipe is removing well-mixed solution from the tank at a rate of 2 gallons per minute. What is the differential equation whose solution is a function S(t) which gives the amount of sugar dissolved in the tank at time t. sugar. А pipe dS 3. 2S 47-2t dS 3. 47+2t dS dt 24 2S 94+2t 2S dS dt 24 47+2t * = 24 2S 47-2t %3| dt || || ||

A 94 gallon tank is half full of water and 9 pounds of is pumping water with a concentration 6 pounds of sugar per gallon into this tank at a rate of 4 gallons per minute. A second pipe is removing well-mixed solution from the tank at a rate of 2 gallons per minute. What is the differential equation whose solution is a function S(t) which gives the amount of sugar dissolved in the tank at time t. sugar. А pipe dS 3. 2S 47-2t dS 3. 47+2t dS dt 24 2S 94+2t 2S dS dt 24 47+2t * = 24 2S 47-2t %3| dt || || ||

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A 94 gallon tank is half full of water and 9 pounds of sugar. A pipe
is pumping wvater with a concentration 6 pounds of sugar per gallon
into this tank at a rate of 4 gallons per minute. A second pipe is
removing well-mixed solution from the tank at a rate of 2 gallons per
minute. What is the differential equation whose solution is a function
S(t) which gives the amount of sugar dissolved in the tank at time t.
dS
dt
2S
47-2t
d.S
dt
3.
2
2.S
47+2t
dS
dt
24 -
2S
94+2t
dS
dt
24
2S
47+2t
2S
dS
dt
24 –
%3D
47– 2t
||

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27
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