Jianlin and I have written up solutions to the review problem!
My solutions are posted at:
http://www.me.berkeley.edu/~watchwrk/math128a/rehersalsolutions.pdf
Jianlin's solutions are posted at:
http://socrates.berkeley.edu/~math/rehearsalsol.pdf
I made a MISTAKE when I went over the last part of this problem in my
office hours on Wednesday. My apologies. The difference equation from
the first part of the problem has characteristic values with modulus
greater than 1, and so without really thinking I called the method
unstable. This is WRONG; please read through my posted solutions for a
careful correct treatment of the problem. As always, please email me
with any questions or concerns, or come to my office hours next week.
cheers, :-)
~Patch