1) Write all the calculations needed to show how to find all positive eigenvalues, A > 0, and eigenfunctions y(x) solutions of the eigenfunction problem -y" = y, y(0) = 0, y' (7) = 0. Label the eigenfunctions with an index n = = 1, 2, 3,.. 2) Show, with an explicit calculation, that the eigenfunction with n = 1 is orthogonal to the eigenfunction with n = 2. Hint: The following trigonometric identities may or may not be useful, 11 sin(a) sin(B) = (cos(a - b) - cos(a + B)), 2 1 cos(a) cos(B) = (cos(a - b) + cos(a + B)). 2