TIFR System Science 2018 Question 1

Question

Consider a discrete-time system which in response to input sequence x[n] (n integer)
outputs the sequence y[n] such that
$y[n] = 0, n = −1, −2, −3,...$
and $y[n]=2 (y[n − 1] + nx[n]), n = 0, 1, 2,...$. Find out if the system is linear and time-invariant.