If a diver of mass m stands at the end of a diving board with length L and linear density ρ, then the board takes on the shape of the graph of y = f(x),where EIy ″ = mg(L − x) +1/2 ρg(L − x)2. E and I are positive constants that depend on the material of the board, and g (< 0) is the acceleration due to gravity. The x y coordinate plane is given. A diving board modeled by a function graph starts at the origin nearly horizontal, goes down and right becoming more steep, and stops in the fourth quadrant. A diver stands with feet at the right end of the board. (a) Find an expression for the shape of the curve. f(x) = y =  Use f(L) to estimate the distance below the horizontal at the end of the board. −f(L) =

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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.