Math 4791/5791 - Problem Set 8
Fall 1998

Due November 3

1. Read the notes on difference equations and then work on the following problems. Remember that with difference equations, it's always easy to check your solutions.
2. Solve the initial value problem

   

3. The Fibonacci sequence is generated by the difference equation

   

   Find the solution of this initial value problem and verify (unlikely as it seems) that this solution actually generates the Fibonacci sequence. What is the ratio of successive Fibonacci numbers as (that is, )?

4. Solve the initial value problem

   

   (Proceed by analogy with the repeated roots case of ODEs.)

5. *Solve the initial value problem

   

   (Proceed by analogy with the complex roots case of ODEs.)