A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response $$y\left( t \right) = t{e^{ - t}},\,\,t > 0.$$ The transfer function of the system is:

The impulse response of an initially relaxed linear system is $${e^{ - 2t}}u\left( t \right).$$ To produce a response of $${te^{ - 2t}}u\left( t \right),$$ the input must be equal to