Suppose an input f$($t$)=$t$,$ when applied to a linear system, produces the output

y$($t$)=2($e$-$t$-1)+$t$($e$-$t$+1),$t$0.$

$1)$ What is the system transfer function $($s$)?$

$2)$ Use the system transfer function to determine the output if a Heaviside unit step input f$($t$)=$h$($t$)$ is applied to the system.

Recall that the system transfer function is $($s$)=$Y$($s$)$F$($s$)$

$($s$)=(2(1$s$+11$s$)+1($s$+1)2+1$s$2)1$s$2$Correct $$

y$($t$)=$