Using principles from physics it can be shown that when a

Chapter 3, Problem 3.647

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Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve that satisfies the differential equation where is the linear density of the cable, is the acceleration due to gravity, and is the tension in the cable at its lowest point, and the coordinate system is chosen appropriately. Verify that the function is a solution of this differential equation

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