A pool has a volume of 1000?3. At time ? = 0 the pool is empty. We then fill the pool with water at a constant speed ? = 2.4 ?3 per minute. At the same time, water leaks out of the pool at a rate that is at all times proportional to the volume of water. The proportionality constant is ? = 3 ∙10^−3 ?????? − 1. Let ? (?) be the volume of water in the pool t minutes after we started filling water in the pool.a) Set up a differential equation that ? (?) must satisfy.b) Solve the equation by the integrative factor method.c) Find when the pool is half full. A pool has a volume of 1000m3. At time t = 0 the poolis empty. We then fill the pool with water at a constantspeed v = 2.4 m3 per minute. At the same time, waterleaks out of the pool at a rate that is at all timesproportional to the volume of water. Theproportionality constantis a = 3 ·10^-3 minutt – 1.Let V (t) be the volume of water in the pool t minutesafter we started filling water in the pool.a) Set up a differential equation that V (t) must satisfy.b) Solve the equation by the integrative factor method.c) Find when the pool is half full.

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Answered: A pool has a volume of 1000m3. At time…

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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A pool has a volume of 1000?3. At time ? = 0 the pool is empty. We then fill the pool with water at a constant speed ? = 2.4 ?3 per minute. At the same time, water leaks out of the pool at a rate that is at all times proportional to the volume of water. The proportionality constant is ? = 3 ∙10^−3 ?????? − 1. Let ? (?) be the volume of water in the pool t minutes after we started filling water in the pool.a) Set up a differential equation that ? (?) must satisfy.b) Solve the equation by the integrative factor method.c) Find when the pool is half full.

A pool has a volume of 1000m3. At time t = 0 the pool
is empty. We then fill the pool with water at a constant
speed v = 2.4 m3 per minute. At the same time, water
leaks out of the pool at a rate that is at all times
proportional to the volume of water. The
proportionality constantis a = 3 ·10^-3 minutt – 1.
Let V (t) be the volume of water in the pool t minutes
after we started filling water in the pool.
a) Set up a differential equation that V (t) must satisfy.
b) Solve the equation by the integrative factor method.
c) Find when the pool is half full.

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