3. Consider the eigenvalue/boundary value problem for y(t): − 3y" + xy = 0, y′(0) = 0, y' (√3)= (a) Is A = 0 an eigenvalue? If it is, calculate the corresponding eigenfunctions. (b) Determine all negative eigenvalues, A< 0, and calculate the corresponding eigenfunc- tions. Clearly show the calculations and state the reasoning justifying your conclusions.

Determine the eigenvalues and corresponding eigenfunctions for the following boundary value problem: Domain xe (0,7) X" + AX = 0 with boundary conditions: X(0)=X'(7)=0

П Write the function f(x) = x (1-x) as an eigenfunction ex- pansion of the eigenfunctions corresponding to the Sturm-Liouville prob- lem y" + Xy = 0, 0 < x < y(0) = 0 y (H) = 0 πT