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10 Only Possible Solution of Affine Difference Equation
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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Preferable reference for this tutorial is
Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\