Signals and Systems - System Properties

The input $x(t)$ and the output $y(t)$ of a system are related as $y(t) = e^{-t} \int_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad -\infty < t < \infty$. The system is

Consider the system with following input-output relation $y[n] = (1+(-1)^n) x[n]$ where, $x[n]$ is the input and $y[n]$ is the output. The system is