For a 2nd order linear ODE,find the interval where some non-trivial solutions remain bounded and some become unbounded

For a 2nd order linear ODE,find the interval where some non-trivial
solutions remain bounded and some become unbounded

$$y^{''}+(2\alpha-3)y^{'}+\alpha(\alpha-3)y = 0$$
Determine all values of $\alpha$, if any, for which some non-trivial
solutions remain bounded and some become unbounded as $t \rightarrow
\infty$.
The general solution I got is
$$y(t) = C_1e^{(3-\alpha)t}+C_2e^{-at}$$
And I think the interval is $(-\infty,3]$, but this is not the correct
answer. Can anyone help me?