These should be sent out a day or two before the consults. You will have about 100 minutes to complete them (likely less if we talk), so do your best to have them solid and up-to-speed on the day-of.
Typo on Q2 solution: should be $y = \int G(x,\xi) f(\xi)/(\xi+3) \, \de{\xi} + x^2/4$ (courtesy of A. David)
Typo on Q1: should be $(1+\alpha)y$ (courtesy of T. Simpkins)
Typo on Q2a: should be $y(2\pi)$ and not $2(2\pi)$ (courtesy of T. Simpkins)
For a nice summary of the Frobenius series result, see this. The excerpt is from Mathematical Methods and Boundary Value Problems by Sam Melkonian.
Post revision notes: There was much confusion about how adjoint boundary conditions were defined. Here is a writeup on defining adjoints.
You can get a pdf version here or click the image for a larger version.