Solving Difference Equations

A common use of the z-transform is to solve difference equations. 76, which is defined in the context 77, solves linear difference equations with constant coefficients:
<#3196#>
verbatim184#
<#3196#>
Here, we have asked for no justification (<#479#>Dialogue -;SPMgt; False<#479#> and implied that the solution is right-sided since the default value of the <#480#>RightSided<#480#> option is <#481#>True<#481#>. Because the solution is assumed to be right-sided, the <#482#>Step<#482#> term in the driving function is not necessary. In this case, a full set of initial conditions is given. In general, initial conditions are optional and the missing ones are considered to be zero. When solving a difference equation, <#483#>ZSolve<#483#> substitutes the initial conditions into the left-hand side of the difference equation. This gives rise to impulse functions on the right-hand side of the difference equation that account for behavior before the driving function turns on. This approach enables the bilateral z-transform to solve the augmented difference equation completely.