The characteristic equation has a repeated root $r = 1$.

The general solution is $a_n = (c_1 + c_2 n) \cdot 1^n = c_1 + c_2 n$.

If $a_0 = 3$ and $a_1 = 5$, then $a_n = 2n + 3$.

The sequence grows quadratically with $n$.