Consider the differential equation

y$^((3))-$y$^(\text{'}\text{'})+4$y$^(\text{'})-4$y$=-48$e$^(-2$t$)-8$

$($a$)$ What is the order of this differential equation?

$($b$)$ Is this equation linear or non$-$linear?

$($c$)$ Does the function y$\_(1)($t$)=$cos$(2$t$)+2$e$^(-2$t$)+2$ solve this differential equation? What about

y$\_(2)($t$)=2$sin$(2$t$)-$e$^($t$)+2?$ Make sure to show all necessary work to reach your conclusion.