Water flows into a reservoir at a rate of 500 + 7t2 gallons/hour. There is a hole in the reservoir and water leaks out at a rate of 4t + t² gallons/hour. What is the net change in the amount of water in the reservoir over the time interval [1,5]?

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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.