$3\mathrm{.}17.$ Consider three continuous$-$time systems $S_1,S_2,$ and $S_3$ whose responses to a complex exponential input $e^{jSt}$ are specified as

$S_1$:$e^{j5t}t{e}^{j5t}$

$S_2$:$e^{j5t}{e}^{j5(t-1)}$

$S_3$:$e^{j5t}$longrightarrowcos$(5t)$

For each system, determine whether the given information is sufficient to conclude that the system is definitely not LTI.