Consider the differential equation

$$y^{\,\prime\prime} + \alpha y^{\,\prime} + \beta y = t + e^{3 t}.$$
Suppose the form of the particular solution to this differential equation as prescribed by the method of undetermined coefficients is

$$y_p(t) = A_1 t^2 + A_0 t + B_0 t e^{3 t}.$$
Determine the constants $\alpha$ and $\beta$.

$\alpha =$ help (numbers)
$\beta =$ help (numbers)