In problem the eigenvalues and eigenfunctions of the boundary-value problem y'' + y = 0, y'(0) =

In problem the eigenvalues and eigenfunctions of the boundary-value problem y'' + λy = 0, y'(0) = 0, y'(π) = 0 are λ_n = n², n = 0, 1, 2, . . . , and y = cos nx, respectively. Fill in the blanks.

A solution of the BVP when λ = 36 is y = ______ because ____.