9.2 Exercises on second-order difference equations

1. Solve the following difference equations and determine whether the solution paths are convergent or divergent, oscillating or not.
   1. x_t+2 + 3x_t+1 − (7/4)x_t = 9.
   2. x_t+2 − 2x_t+1 + 2x_t = 1.
   3. x_t+2 − x_t+1 + (1/4)x_t = 2.
   4. x_t+2 + 2x_t+1 + x_t = 9·2^t.
   5. x_t+2 − 3x_t+1 + 2x_t = 3·5^t + sin((1/2)πt).

[Solutions]