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 d'y pg dy 2 1 + dx dx2 where p is the linear density of the cable, g is the accelera- tion due to gravity, T is the tension in the cable at its lowest point, and the coordinate system is chosen appro- priately. Verify that the function T cosh Pg pgx y = f(x) T is a solution of this differential equation.

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 d'y pg dy 2 1 + dx dx2 where p is the linear density of the cable, g is the accelera- tion due to gravity, T is the tension in the cable at its lowest point, and the coordinate system is chosen appro- priately. Verify that the function T cosh Pg pgx y = f(x) T is a solution of this differential equation.