Consider a cable fixed at the points (0,O) and (l,h). It carries a load along the y-axis, distributed as To find the shape of this cable we have to solve the variational problem with the boundary...

Consider a cable fixed at the points (0,O) and (l,h). It carries a load along the y-axis, distributed as

To find the shape of this cable we have to solve the variational problem

with the boundary conditions

y(0) = 0 and y(l) = h.

Find the shape of the wire accurate to second order.