Let a, b and w be constants, with w # 0. (a) Show that the Euler-Lagrange equation for the functional Sly] = dx (y"? + way? + 2y(asinwx + bsinh wx)) , y(1) = 0, y(2) = 1, is y" -wy = asinwx + bsinhwx, y(1) =0, y(2) = 1. (b) Solve this equation to show that the stationary path is a sin wr br cosh wr y = a sinh (w(x - 1)) + 8 sinh (w(x - 2)) - 2w2 + 2w where 1 a sin 2w b cosh 2w Of = 1 + sinh w 2w2 W 1 b cosh w a sin w B = sinh w 2w 242 (c) Determine whether Sly] has a maximum or a minimum on this stationary path, and whether it is global or local