Consider the linear operator L$($y$)=$y$6$y$+9$yL$($y$)=$y$6$y$+9$y$.$

$1)$ Find the correct, final guess, for a particular solution yp$($t$)$yp$($t$)$ of the differential equation L$($y$)=$e$5$tL$($y$)=$e$5$t$.$

Note: The kk$$s below denote arbitrary constants.

A$.$ yp$($t$)=$ke$3$typ$($t$)=$ke$3$t

B$.$ yp$($t$)=$kt$2$e$5$typ$($t$)=$kt$2$e$5$t

C$.$ yp$($t$)=$kte$3$typ$($t$)=$kte$3$t

D$.$ yp$($t$)=$ke$5$typ$($t$)=$ke$5$t

E$.$ yp$($t$)=$k$1$e$3$t$+$k$2$e$5$typ$($t$)=$k$1$e$3$t$+$k$2$e$5$t

F$.$ yp$($t$)=$kt$2$e$3$typ$($t$)=$kt$2$e$3$t

G$.$ yp$($t$)=$kte$5$typ$($t$)=$kte$5$t

H$.$ None of the above.