# Difference equation: when to use iteration and when the general method?

This question may sound weird. I'm attending a course of growth economics and our professor taught us some simple rules about difference equations. He taught us two different methods, but didn't tell us when to use the first one and when to use the other one. In the first case, when we have something like

$y_t = y_{t-1} + h$ we solve with $y_t = y_0 + th$

and when

$y_t=b y_{t-1}$ we get $y_t =b^t y_0$

So when $\boldsymbol{y_t = y_{t-1} + 6}$, the solution is $y_t = y_0 + 6t$

But when we have something like $\boldsymbol{y_{t+1} = 2y_t - 2}$

we have to solve it with a more complex procedure, finding the general and the particular integrals.

I don't understand if the difference between the two "exercises". Is it just in the fact that the second one has a coefficient attached to $y_t$?

Thank you in advance!

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## 1 Answer

I think you can find the answer to your question in this document (p. 222 and following pages)

http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/discrete_ch14.pdf

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Could you add some more context beyond a link? –  Daniel Rust Jul 23 '13 at 14:24