Consider the boundary' value problem - u" = f(x), u(0) = 0, u(l) = 2u'(l).
(a) Find the Green's function.
(b) Which of the fundamental properties does your Green's function satisfy?
(c) Write down an explicit integral formula for the solution to the boundary value problem, and prove its validity by a direct computation.
(d) Explain why the related boundary value problem - u" = f, u(0) = 0. u(1) - u (l). Does not have a Green's function.