Find the eigenfunctions of the Sturm-Liouville problem y" + y = 0, y(0) = 0, y' (L) = 0, and make the set an orthonormal set of eigenfunctions.

Can I get help with this "complex eigenvalues and eigenvectors" problem?

Find the eigenvalue and eigenfunctuons of the Sturm-Liouville problems:  (xy')'+(lamda/x)y=0, y(1)=y(e^2)=0

Find the eigenvalues and eigenfunctions of the boundary value problem у" + 1у %3D 0, у (0) — у(2п), у'(0) — у'(2п). Evaluate all cases.

3. Solue the ghen system by using the eigenvalue problem x': x - 5y y'- 2x-y.

The eigenvalues associated with the equation below are all nonnegative. y" + λy = 0;_y'(−π) = 0, y'(0) = 0 First determine whether λ = 0 is an eigenvalue. Then find the positive eigenvalues and associated eigenfunctions. Plot the eigenfunctions, corresponding to n = 1, 2, 3, 4, 5.

Find all solution to the eigenvalue problem -X" = A X. X (-L) = X (L) & X'(-L) = X'(L)