The response of a discrete time system \(y[n]\) obeys the following relation:
\[ y[n]=\frac{5}{6}y[n-1]-\frac{1}{6}y[n-2]+x[n]. \] The input to the system is \(x[n]=\delta[n]-\frac{1}{3}\delta[n-1]\). Which of the following options is TRUE for \(y[n]\)?