Chapter 4.3, Problem 48P

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 $t\to \infty$.

$y^{″}+\left(3-\alpha \right)y^{\prime }-2\left(\alpha -1\right)y=0$