# Determine if $y[n] = ny[n-1] + x[n]$ is linear time invariant and BIBO stable

Check if the following system is linear time invariant and BIBO stable.. $$y[n] = ny[n-1] + x[n]$$

for $n\ge 0$. We are also given that the system is at rest (i.e. $y[−1] = 0$).

I know that to show linearity, we show that $H[ax_1 + bx_2] = aH[x_1] + bH[x_2]$ except that the question has a $y[n-1]$ on the RHS which is throwing me off.