Chapter 4.3, Problem 47P

In each of Problems $47$ and $48$, determine the values of $\alpha$, if any, for which all solutions tend to zero as $t\to \infty$; also determine the values of $\alpha$, if any, for which all (nonzero) solutions become unbounded as $t\to \infty$.

$y^{″}-\left(2\alpha -3\right)y^{\prime }+\alpha \left(\alpha -3\right)y=0$