so I'm finding trouble in verifying a solution I have found for first order homogeneous and inhomogeneous difference equations. I can find the solutions fine, but it is verifying them through substitution (i.e LHS = RHS) that I have trouble with. Especially with what to do on the LHS.
- Where does the $+1$ come from on the left-hand side? I feel like it is coming from nowhere?
- For the second example, what do I do on the left-hand side? Substitute my solution into the left-hand side? I just put it there and then what? How does it change? I am so confused.
Thanks so much to anyone who can help me!