A tank initially has 100 gallons of brine containing 5 Ibs of salt. The mixture is kept well-mixed. A solution with3 Ibs salt/gal is allowed to flow into the tank at a rate of 2 gal/min, and the mixture flows out of the tank at arate of 2 gal/min.Sketch a picture and define your variables.Set up the DE that fits this situation, and simplify your DE. Be sure to use proper notation. You do NOT haveto solve the DE.What type of DE is this? (Integrate, separable, linear, linear inside, homogeneous, Bernoulli, or exact?)What is the initial condition that would help you find the IVP solution?

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A tank initially has 100 gallons of brine containing 5 lbs of salt. The mixture is kept well-mixed. A solution with 3 Ibs salt/gal is allowed to flow into the tank at a rate of 2 gal/min, and the mixture flows out of the tank at a rate of 2 gal/min.

A tank initially has 100 gallons of brine containing 5 lbs of salt. The mixture is kept well-mixed. A solution with 3 Ibs salt/gal is allowed to flow into the tank at a rate of 2 gal/min, and the mixture flows out of the tank at a rate of 2 gal/min.

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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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 tank initially has 100 gallons of brine containing 5 Ibs of salt. The mixture is kept well-mixed. A solution with
3 Ibs salt/gal is allowed to flow into the tank at a rate of 2 gal/min, and the mixture flows out of the tank at a
rate of 2 gal/min.
Sketch a picture and define your variables.
Set up the DE that fits this situation, and simplify your DE. Be sure to use proper notation. You do NOT have
to solve the DE.
What type of DE is this? (Integrate, separable, linear, linear inside, homogeneous, Bernoulli, or exact?)
What is the initial condition that would help you find the IVP solution?

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