Problem about rope (nonlinear equation)

[fabio]

I would like an aid in the following problem(a tip):

Find the equation of motion of a homogeneous rope, knowing that the tension is not more constant and that each element of mass carries through only vertical displacements. It does not make the approach of small displacements and considers the weight of the rope assuming the constant local gravitation. The resultant equation is a nonlinear equation.

 

[quasar987]

What is the setting? In what situation is the rope?