When a cable is hung between two poles, it takes the shape of a curve y = f(x) that satisfies the differential equations:

a(d2^2y/dx^2) =1+(dy/dx)^2

where a is a constant that depends on the lienar density of the cable, the gravitational acceleration, and the tension in the cable at its lowest point. SHow that the function is a solution of the differential equation.

f(x) = acosh(x/a)