A tank contains 220 gallons of water and 45 oz of salt. Water containing a salt concentration of (1/4)(1+(1/5)sint) oz/gal flows into the tank at a rate of 6 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?

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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.