In each of Problems 1-10, find the eigenvalues and eigenfunctions of the regular or periodic Sturm- Liouville problem, and list a complete set of eigenfunctions. 1. y" + y = 0; y(0) = y' (L) = 0 2. y" + y = 0; y'(0) = y' (L) = 0 3. y" y = 0; y'(0) = y(4) = 0 y = 0; y(0) = y(), y'(0) = '() 4. y" + 5. y+y=0; y(-3) = (3), '(-3) = '(3) 6. y" + y = 0; y(0) = 0, y() +2' () = 0 7. y" + y = 0; y(0) - 2y'(0) = 0, y' (1) = 0 8. y" + 2y + (1+)y = 0; y(0) = y(1) = 0 9. (exy')'+ey = 0; y(0) = () = 0 10. (exy')' + (1+)e-6xy = 0; y(0) = y(8) = 0 11. Let n = 1-1/n for n = 1, 2,... Show that cannot be a regular or periodic Sturm-Li problem having these numbers as eigenvalue