Using Z transforms to solve difference equations.

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Uan
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Hi,

We can use Laplace transforms to solve DEs with these guys:

Two Laplace transform identities: L{y'} = sY(s) - y(0) and L{y''} = s^2 Y(s) - sy(0) - y'(0), written as typeset equations.


But what are the z transform versions in discrete time that include initial conditions, and how do you derive them? For example y[n+1], y[n+2] etc.

Thanks