A bar of length i = 1 and stiffness function c(x) = 1 +x has both ends

Question:

A bar of length i = 1 and stiffness function c(x) = 1 +x has both ends clamped: n(0) = «(1) = 0.
(a) Construct the Green's function for this boundary value problem.
(b) Use the Green's function to construct an integral formula for the solution when the bar is subject to a general external force /(x).
(c) Evaluate the integrals and compare with your solution in Exercise 11.1.4 in the case of a unit gravitational force f(x)= 1.