Dear all, the following ar Berkely problem (Spring 85).

Let http://math.berkeley.edu/~desouza/Pr...ng85/img45.gif be given. Consider the linear difference equation

(Note the analogy with the differential equation http://math.berkeley.edu/~desouza/Pr...ng85/img47.gif.)

- Find the general solution of http://math.berkeley.edu/~desouza/Pr...ng85/img48.gif by trying suitable exponential substitutions.
- Find the solution with http://math.berkeley.edu/~desouza/Pr...ng85/img49.gif and http://math.berkeley.edu/~desouza/Pr...ng85/img50.gif. Denote it by http://math.berkeley.edu/~desouza/Pr...ng85/img51.gif,

http://math.berkeley.edu/~desouza/Pr...ng85/img52.gif.- Let http://math.berkeley.edu/~desouza/Pr...ng85/img53.gif be fixed and http://math.berkeley.edu/~desouza/Pr...ng85/img54.gif. Show that