20 4(5x4)(eigenvalue is 4) B() is an eigenfunction of A(vi dx2- 2x dx b(= (48x2-24)-2x(16x3-24x) 48x2-24-32x4+48x2 -32x4+96x2-24 8(4x4-12x2+3)(eigenvalue is-8) B(iv )is an eigenfunction of A(v. x dx2 +(I-x)dx B(iv) x(2)+(1-x)(2x-4) 2x+2x-4-2x2+4x 2x2+8x-4 -2(x2-4x +2)(eigenvalue is-2)10 20x4 4(5x4) (eigenvalue is 4) B(i.) is an eigenfunction of A(vi.): d2 dx2 - 2x d dx B(i) = (48x2 - 24) - 2x (16x3 - 24x) 48x2 - 24 - 32x4 + 48x2 -32x4 + 96x2 - 24 -8(4x4 - 12x2 + 3) (eigenvalue is -8) B(iv.) is an eigenfunction of A(v.): x d2 dx2 + (1-x) d dx B(iv.) = x (2) + (1-x) (2x - 4) 2x + 2x - 4 - 2x2 + 4x -2x2 + 8x - 4 -2(x2 - 4x +2) (eigenvalue is -2) 5