Problem about rope (nonlinear equation)

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

Thread 'Modeling a graph that shows age in relation to depth of an ice sample'

To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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