Solve questions 1,3,5,7,9

In each of Problems 1-10, find the eigenvalues and 6. y" + xy = 0; y(0) = 0, y(IT) + 2y' (IT) = 0 eigenfunctions of the regular or periodic Sturm- 7. y" + Ay = 0; y(0) - 2y' (0) = 0,y'(1) = 0 Liouville problem, and list a complete set of eigenfunctions. 8. y" + 2y' + (1 + 2)y = 0; y(0) = >(1)=0 1. y" + ay = 0; y(0) = y'(L) = 0 9. (ezxy')' + hetty = 0; y(0) = y(IT) =0 2. y" thy = 0; y' (0) = y'(L) = 0 10. (e oxy')' + (1 + x )e-6xy = 0; y(0) = >(8) =0 3. y" tay = 0;y' (0) = >(4) = 0 11. Let An = 1 - 1 for n = 1, 2, . ... Show that cannot be a regular or periodic Sturm-Li 4. y" + hy = 0; y(0) = y(IT), y' (0) = y'(IT) problem having these numbers as eigenvalue 5. y" + ay = 0; y(-3) = y(3), y'(-37) = y'(351)