Question $1$: Constant Coefficient Linear ODE

Find the general solution of d$3$ydt$34$d$2$ydt$2+4$dydt$=0$

$($a$)$

y$($t$)=$A$+$Be$4$t$+$Ce$4$t with A$,$ B$,$ and C arbitrary constants

$($b$)$

y$($t$)=$Ae$4$t$+$Be$4$t with A and B arbitrary constants

$($c$)$

y$($t$)=$A$+$Bt$+$Ct$2$ with A$,$ B$,$ and C arbitrary constants

$($d$)$

y$($t$)=$A$+$Be$2$t$+$Ce$2$t with A$,$ B$,$ and C arbitrary constants

$($e$)$

y$($t$)=$A$+$Be$2$t$+$Cte$2$t with A$,$ B$,$ and C arbitrary constants

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