Differential Equation Mixing Problem: Solution by Integrating Factor, Slope Field, Euler's Method
A 100 gallon tank (or "vat") initially has 10 gallons of pure water. Salt water with concentration 2 pounds per gallon is entering the tank at 6 gallons per minute, while a well-mixed solution is exiting the tank at 4 gallons per minute. What is the amount of salt in the tank when it fills? This is a mixing problem. Use the fact that the rate of change dS/dt = Rate In - Rate Out. Multiply the concentrations by the flow rates to find these rates. We get a first-order differential equation that can be solved by the Method of Integrating Factors. We graph the solution in the slope field using Wolfram Mathematica. Then we also use NestList in Mathematica to implement Euler's Method for a numerical solution and look at the errors in the method. 🔴 Burden, Faires, Burden "Numerical Analysis": https://amzn.to/3DBvCWn
Numerical Analysis, Class 24A
#NumericalAnalysis #DifferentialEquations #IntegratingFactor #Mathematica #EulerMethod #MixingProblem
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