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A pond contains V gallons of water and M grams of pollutant. Polluted water, containing ρ...

A pond contains V gallons of water and M grams of pollutant. Polluted
water, containing ρ grams per gallon of the pollutant, enters the pond at the rate of a gallons per hour. The mixture flows out at the same rate of a gallons per hour, and we assume that the pollutant is always perfectly mixed with the water in the pond (that is, equal volumes of water contain the equal amount of pollutant everywhere in the pond). Write the differential equations for the amount of pollutant in the pond, as a function of time, and investigate the long-time behavior of the solution.
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