Question: This is on the application of first-order differential equations , specifically targeting: mixing phenomena (First Order Linear Differential Equations - FOLDE Application) A tank is

This is on the application of first-order differential equations, specifically targeting: mixing phenomena (First Order Linear Differential Equations - FOLDE Application)

A tank is utilized for mixing sugar solutions which can initially contain 80 gallons of water. A sugar-water containing 1.5 lbs of sugar per gallon enters the tank at a rate of 2 gallons per minute. The tank is kept well mixed. Sugar-water is pumped out of the tank at 3 gallons per minute. Find the amount of sugar in the tank after 10 minutes?

a. What is the working equation for the mixing problem? b. What is the linear form of the differential equation? c. What is the integrating factor for the d.e.? d. What is the general solution for the differential equation? e. What is the first boundary condition to determine C? f. What is the particular equation for the problem? g. What is the amount of sugar in the tank after 10 minutes?

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