A large tank contains 50 gallons of water into which 5 pounds of salt has been dissolved. A solution containing 2 pounds of salt per gallon is pumped into the tank at the rate of 4 gal/min. The well stirred mixture is pumped out at the slower rate of 3 gal/min. Find the number of pounds of salt X(t) in the tank at time t.

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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.