We have characteristic polynomial \(x^2 - 2x + 1\text{,}\) which has \(x = 1\) as the only repeated root. Thus using the characteristic root technique for repeated roots, the general solution is \(a_n = a + bn\) where \(a\) and \(b\) depend on the initial conditions.
\(a_n = 1 + n\text{.}\)
For example, we could have \(a_0 = 21\) and \(a_1 = 22\text{.}\)
For every \(x\text{.}\) Take \(a_0 = x-9\) and \(a_1 = x-8\text{.}\)