Consider the functional f[1+ y2/y]dx, y(0)=1. Find the admissible extremals satisfying: (a) no additional constraint; (b) the essential boundary condition y(1) = 4; (c) the natural boundary condition at x = 1; (d) the transversal boundary condition on C: y = 4. Bonus. We showed in class that Fy is continuous for all extremals but that's not true here. Explain.