Consider the following systems with the initial conditions.
1. y(n)−.6y(n−1)=0,y(−1)=1
2. y(n)−.6y(n−2)=0,y(−1)=0,y(−2)=1
3. y(n)−.6y(n−1)+.6y(n−2)=0,y(−1)=0,y(−2)=−1
4. y(n)−.1y(n−3)=0,y(−1)=y(−2)=0,y(−3)=1
5. y(n)+.1y(n−1)+y(n−3)=0,y(−1)=0,y(−2)=1,y(−3)=0
6. y(n)+.6y(n−2)=0,y(−1)=y(−2)=1
Are the above systems stable? What is the output due to the given initial conditions?