Discrete dynamic behavior is characterized by discrete difference equations. A general n^th-order, linear, variable coefficient, nonhomogeneous difference equation can be written as

Analogous to the continuous form, the general solution for y(k) is constructed as a linear combination of a homogeneous and particular solution, or

Again, analogous to the continuous case, linear difference equations with constant coefficients have relatively simple homogeneous solutions. Given the homogeneous equation

assume a solution of the form

for some constant l . Now, performing the appropriate substitutions gives

or

Finally, letting , we can construct a general solution to eqn (2.10) with a linear combination of (for distinct roots), giving

The situation for repeated roots and for the determination of particular solutions is similar to that for continuous systems.