18. Solve the BVP by determining the appropriate Green's function, expressing the solution as a definite integral. -y" = f(x), y(0) + y'(0) = 0, y(1) + y'(1) = 0. 19. 20. 21. Consider the initial value problem : y' f(x,y), y(0) = 1 where f(x,y) = xy + y, (x,y) = D with D : = [-2,2] X [-1,3]. Show that f(x,y) is bounded and statisfies a Lipschitz condition with respect to y on D and determine a bound and Lipschitz constant on D. Further, determine h, as required in the Picard's Theorem, for a unique solution of the initial value problem to exist on x