Find the eigenvalues and eigenfunctions of the given boundary-value problem. Use a CAS to approximate the first four eigenvalues λ₁, λ₂, λ₃, and λ₄.

y⁽⁴⁾ – λy = 0, y(0) = 0, y'(0) = 0, y(1) = 0, y'(1) = 0

Consider only λ = α⁴, α > 0.