A tank initially contains 100 gal of brine in which 50 lb of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 4 gal/ min. a. At what rate (pounds per minute) does salt enter the tank at time t? b. What is the volume of brine in the tank at time t? c. At what rate (pounds per minute) does salt leave the tank at time t? d. Write down and solve the initial value problem describing the mixing process. e. Find the concentration of salt in the tank 25 min after the process starts.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.