Solving Difference Equations using a TiNspire CX CAS can be done using the Differential Equations Made Easy app as shown below :
Select either 1. or 2. order Difference Equations:

Say, we start with a 1. order Difference Equation, we enter the coefficients a , b and c and the initial value y(0) as shown in image below:

Plugging in the given values into the general solution yields:

Lets also take a look at a 2. order Difference Equation:

How nice is this? Solutions to any 1. and 2. order Difference Equations can be found using the handy TiNspire CX CAS , and using the Differential Equations Made Easy app at www.tinspireapps.com