Question 1:
1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.
2. Use the integral inner product to verify the orthogonality of the eigenfunctions.
y" + λy = 0, y (0) = 0, y (3) = 0
Question 2:
1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.
2. Use the integral inner product to verify the orthogonality of the eigenfunctions.
y" + λy = 0, y'(0) = 0, y'(Π/2) = 0
Question 3:
1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.
2. Use the integral inner product to verify the orthogonality of the eigenfunctions.
y'' + λy = 0, y (0) =0, y' (4) =0