$5[30$ pts $]$ Solve the following differential equations using the method of undetermined coefficients.

$($a$)y^{\text{'}\text{'}}+y^{\text{'}}-6y=12(e^{3t}+e^{2t})$

$($b$)y^{\text{'}\text{'}}+3y^{\text{'}}+2y=sin(3t)+e^{3t}$

$($c$)y^{\text{'}\text{'}}-6y^{\text{'}}+9y=e^{3t}$

$($d$)y^{\text{'}\text{'}}+2y^{\text{'}}+5y=4e^{-t}cos(2t)$