Z-transform of difference equation with initial conditions

1. What is the formula for Z transform?
2. How do you write a difference equation?

What is the formula for Z transform?

Concept of Z-Transform and Inverse Z-Transform

X(Z)|z=ejω=F. T[x(n)].

How do you write a difference equation?

A first-order difference equation only contains the first difference of a variable between two consecutive periods, like y(t + 1) − y(t). A second-order difference equation also contains the second difference in a variable between every two successive time periods, like y(t + 2) − y(t).