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

Transcribed Image Text:

d'y dx dy dx -b, h) (b, h) (0, a) -b