Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve $ y = f(x) $ that satisfies the differential equation
$ \frac {d^2 y}{dx^2} = \frac {pg}{T} \sqrt {1 + (\frac {dy}{dx})^2} $
where $ p $ is the linear density of the cable, $ g $ is the acceleration due to gravity, $ T $ is the tension in the cable at its lowest point, and the coordinates system is chosen appropriately. Verify that the function
$ y = f(x) = \frac {T}{pg} \cosh (\frac {pgx}{T}) $
is a solution of this differential equation.