When a flexible cable of uniform density is suspended between two fixed points and hangs of its own weight, the shape of the cable must satisfy a differential equation of the form 100% y f x d2 y dx 2 k 1 dy dx 2 where is a positive constant. Consider the cable shown in the figure. (a) Let in the differential equation. Solve the resulting first-order differential equation (in ), and then integrate to find . (b) Determine the length of the cable. z dydx z y x b 0 y _b (0, a) (_b, h) (b, h)

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