Undetermined Coefficients

Refer to the following table to find the general equation for $y_p$ based on $g(x)$:

$g(x)$	$y_p$
$P_n(x)$	$t^s Q_n(x)$
$P_n(x) e^{\alpha x}$	$t^s Q_n(x) e^{\alpha x}$
$P_n(x) e^{\alpha x} (\sin \beta t + \cos \beta t)$	$t^s e^{\alpha x} (Q_n(x) \sin \beta x + R_n(x) \cos \beta x)$

Where $s$ is the smallest integer $\ge 0$ s.t. $y_p$ is not a solution to $L[y]=0$ and $P_n(x), Q_n(x), R_n(x)$ are polynomials of degree n.

Then plug into $L[y_p]=g(t)$ and solve for the coefficients.