2) Green function and Fredholm: Seek a solution to the equation dx 2 d'y = f (x), * 6 [0, 1 ] with inhomogeneous boundary conditions y'(0) = Fo, y'(1) = F1. Observe that the corre- sponding homogeneous boundary condition problem has a zero mode. Therefore the solution, if one exists, cannot be unique. a) Show that there can be no solution to the differential equation and inhomogeneous boundary condition unless f (x) satisfies the condition J. " f( ) da = Fo - F . ( x ) [5 points] b) Let G(x, {) denote the modified Green function G (x , 5 ) = - 2 + 22+52, 5