Show that $Y_1[t]- Y_2[t] to 0$ as long as $t to infty$ – Differential equations

Let the differential equation $L[y] = a y” + by’ + cy = g(t)$, where $a$, $b$ and $c$ are strictly positive numbers. If $Y_1(t)$ and $Y_2(t)$ are solutions at the $L[y]$ equation, show that $Y_1[t]- Y_2[t] to 0$ as long as $t to infty$.

I know that $Y_1[t]- Y_2[t]$ has to be a solution of $L[y] =0$. I think I have to use the discriminant $b^2-4ac > 0$. However, it’s not clear that $b^2 > 4ac$.

Is anyone could give me a good hint?