The following Sturm-Liouville problem is given: y '' + 2y '+λy = 0 , in the range 0 < x < 1, with boundary conditions y(0) = 0, y(1) = 0.
a. Write the equation in Sturm-Liouville form and identify the weight function.
b. Solve the problem, that is, identify all the eigenfunctions and their eigenvalues.
c. Verify by direct evaluation that the inner product of the two eigenfunctions with lowest eigenvalues vanish.