$In$ this problem you will use variation $of$ parameters $to$ solve the nonhomogeneous equation

$t^2{y}^{\text{'}\text{'}}-3t{y}^{\text{'}}+3y=2t^3-3t^2$

$A.$ Plug $y=t^{n}2t^3-3t^{2}t$ and $nt,or$ webwork won't accept your answer!$nt0to$ cancel out the $tn,$ which give two fundamental solutions $of$ the form $y=t^n.$

$y_1,=,y_2=$

$W(y_1,y_2),=,$

$C.To$ use variation $of$ parameters, the linear differential equation must $be$ written $in$ standard form $y^{\text{'}\text{'}}+p{y}^{\text{'}}+qy=g.$

What $is$ the function $g?$

$g(t)=$

$D.$ Compute the following integrals.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y_{1}g}{W}dt=$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y_{2}g}{W}dt=c_1$ and $c_{2}y=$

$If$ you don't get this $in3$ tries, you can get a hint $to$ help you find the fundamental solutions.