Linear & nonlinear shooting and linear & nonlinear finite difference methods

hsong9

1. The problem statement, all variables and given/known data
Boundary value problem
y'' = 5sinh(5y), 0<x<=1
y(0)=0, y(1) = 1.

2. Relevant equations
3. The attempt at a solution

I have to determine a one method of some methods (see titles) to solve the boundary problem. I am not sure how I choose it.
Anybody help?