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10 Possible Solutions of Affine Difference Equation

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The ten possible types of solutions to affine difference equation  are sorted in the table below.

No

Type of Solution

 

Cases

1.

Constant

* ,

* ,

,

,

* ,

,

2.

Linearly increasing without bound

,

3.

Linearly decreasing without bound

,

4.

Exponentially increasing without bound

* ,

5.

Exponentially decreasing without bound

* ,

6.

Exponentially increasing to a bound

,

7.

Exponentially decreasing to a bound

,

8.

Oscillating with constant amplitude

* ,

* ,

9.

Oscillating with increasing amplitude

* ,

* ,

10.

Oscillating with decreasing amplitude

,

,


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