The continuous LTI system is described by
\(\frac{{dy}}{{dt}} + 2y\left( t \right) = x\left( t \right)\)
Using the Fourier transform, for x(t) = e-t u(t), the output y(t) will be1
(e-t – e2t) u(t)
2
(et + e-2t) u(t)
3
(e-t – e-2t) u(t)
4
(et + e2t) u(t)