$(3D^2+D-14)y =13e^{2x}$
$P.I= \large\frac{13 e^{2x}}{3D^2+7D- 6D-14}$
$\qquad= \large\frac{13 e^{2x}}{3D^2+7D-6D-14}$
$\qquad=\large\frac{13 e^{2x}}{D(3D+7) -2(3D+7)}$
$\qquad= \large\frac{13}{6+7}. \frac{e^{2x}}{D-2} $
$\qquad= xe^{2x}$
Hence 3 is the correct answer.