A tank initially contains 400 litres of liquid A. Liquid B is pumped into the tank at the rate of 20 litres per minute. The contents of the tank is pumped out at the same rate of 20 litres per minute. The mixture is stirred continuously and the tank is kept full at 400 litres at all times. Let X (t) denote the amount (in litres) of liquid A in the tank after t minutes. (2.1) Write down the differential equation for X (t) , and its initial value. (2.2) Solve the initial value problem in (a) to find the solution X (t) for all t. (2.3) How long does it take until the tank contains the same amount of both liquid A and liquid B?

A tank initially contains 400 litres of liquid A. Liquid B is pumped into the tank at the rate of 20 litres per minute. The contents of the tank is pumped out at the same rate of 20 litres per minute. The mixture is stirred continuously and the tank is kept full at 400 litres at all times. Let X (t) denote the amount (in litres) of liquid A in the tank after t minutes. (2.1) Write down the differential equation for X (t) , and its initial value. (2.2) Solve the initial value problem in (a) to find the solution X (t) for all t. (2.3) How long does it take until the tank contains the same amount of both liquid A and liquid B?

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 contains 400 litres of liquid A. Liquid B is pumped into the tank at the rate of 20 litres
per minute. The contents of the tank is pumped out at the same rate of 20 litres per minute. The
mixture is stirred continuously and the tank is kept full at 400 litres at all times. Let X (t) denote the
amount (in litres) of liquid A in the tank after t minutes.
(2.1) Write down the differential equation for X (t) , and its initial value.
(2.2) Solve the initial value problem in (a) to find the solution X (t) for all t.
(2.3) How long does it take until the tank contains the same amount of both liquid A and liquid B?

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