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A tann ,intially connista of fure water, A solution into the tann at a rate cf 3'gal/ng uxtyre flóws out at ea the same vate A 3 galfnn. Gnd the well-stied ) What ainiħat value problem is sutisfied by The amonnd of salt AcD in the'Fann ad fime t ? 6) What is The actual amount of salt in the fann at trme t? c How much salt is after 20 minuter? レ

A tann ,intially connista of fure water, A solution into the tann at a rate cf 3'gal/ng uxtyre flóws out at ea the same vate A 3 galfnn. Gnd the well-stied ) What ainiħat value problem is sutisfied by The amonnd of salt AcD in the'Fann ad fime t ? 6) What is The actual amount of salt in the fann at trme t? c How much salt is after 20 minuter? レ

Advanced Engineering Mathematics
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 

**Differential Equation Problem: Salt Solution in a Tank** **Problem Description:** A tank initially contains 50 gallons of pure water. A solution containing 0.5 lb/gal of salt is pumped into the tank at a rate of 3 gallons/min. Simultaneously, the well-stirred mixture is pumped out at the same rate of 3 gallons/min. 1. **Formulation:** - What initial value problem is satisfied by the amount of salt \( A(t) \) in the tank at time \( t \)? 2. **Calculation:** - What is the actual amount of salt in the tank at time \( t \)? 3. **Result:** - How much salt is in the tank after 20 minutes? **Note:** This problem involves setting up and solving a differential equation to determine the concentration of salt in the tank over time.
Transcribed Image Text:**Differential Equation Problem: Salt Solution in a Tank** **Problem Description:** A tank initially contains 50 gallons of pure water. A solution containing 0.5 lb/gal of salt is pumped into the tank at a rate of 3 gallons/min. Simultaneously, the well-stirred mixture is pumped out at the same rate of 3 gallons/min. 1. **Formulation:** - What initial value problem is satisfied by the amount of salt \( A(t) \) in the tank at time \( t \)? 2. **Calculation:** - What is the actual amount of salt in the tank at time \( t \)? 3. **Result:** - How much salt is in the tank after 20 minutes? **Note:** This problem involves setting up and solving a differential equation to determine the concentration of salt in the tank over time.
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Let y(t) is the amount of salt in the tank at any time t. 

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