A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 Ib/gal. At time = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank s well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the nitial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.

A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 Ib/gal. At time = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank s well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the nitial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.

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.

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A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 lb/gal. At time
t = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened
at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank
is well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the
initial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.

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