I have the following first-order difference equation
$$y_{t} = \frac{x_{t}}{1-\rho L} + \epsilon_{t}$$
where $L$ denotes the backshift operator, i.e., $L(x_{t}) = x_{t-1}$. I can obtain a solution to this difference equation heuristically, but I am wondering if there is a general procedure. A solution (the solution?) is
$$y_{t} = \sum_{i = 0}^{\infty} \rho^{i}X_{t-i} + \epsilon_{t}$$
I looked in Goldberger's text and couldn't find it there. Any reference is appreciated also. Thanks.
