A boat travels 100 miles upstream against a 10 mile/hour current. When the boat's velocity is v mile/hour, the number of gallons of gasoline con- sumed each hour is directly proportional to v2. (a) If a constant velocity of v mile/hour is maintained, show that the total number of y of gallons of gasoline consumed is given by 100ku? Pv> 10 and some positive constant k. (v – 10)' (b) Find the speed that minimizes the number of gallons of gasoline con- sumed during the trip.

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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.