I can obtain a solution to the following difference equation heuristically, but I was wondering if there is a procedure. The equation is:

$y_{t} = \frac{x_{t}}{1-\rho L} + \epsilon_{t}$, where $L$ denotes the backshift operator so that $L(x_{t}) = x_{t-1}$.

A (or the, I'm not sure ) solution is $y_{t} = \sum_{i = 0}^{\infty} \rho^{i}X_{t-i} + \epsilon_{t}$.

but I expected there is a general-procedure formula. I looked in Goldberger's text and couldn't find it there. Any reference is appreciated also. Thanks.