Answer to Question #140212 in Differential Equations for Gabriel Lukas

Question

c) 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
d
2y
dx2
= k
s
1 + 
dy
dx2
where k is a positive constant. Consider the cable shown in the Figure 1 below.
Figure 1: Cable hanging between two points.
i) Let z =
dy
dx in the differential equation. Solve the resulting first-order differential equa-
tion (in z), and then integrate to find y. [6]
ii) Determine the length of the cable.

Answer 1

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