A tank is filled with 100 gallons of water and initially has

A tank is filled with 100 gallons of water and initially has Q0 pounds of sugar mixed into the solution. One gallon per minute of sugar water with a concentration of 0.5 pounds per gallon are pumped into the tank and disperse evenly. One gallon per minute is also removed from the tank. What are the equilibrium solution(s) to the differential equation?

Solution

let q be the concentration in tank dq/dt = rate of sugar entering -rate of sugar leaving at steady state dq/dt =0 hence rate of sugar entering =rate of sugar leaving =0.5 pounds per min and concentration of sugar in tank is 0.5 pound/gallon total sugar in tank =0.5*100 =50 pounds