Consider the following difference equation. [ y[n]-y[n-1]-2 y[n-2]=x[n]+2 x[n-1] ] The initial conditions are (y[-1]=1) and (y[-2]=2).
Question:
Consider the following difference equation.
\[
y[n]-y[n-1]-2 y[n-2]=x[n]+2 x[n-1]
\]
The initial conditions are \(y[-1]=1\) and \(y[-2]=2\). The input \(x[n]=u[n]\). Find
(a) Zero input response,
(b) Zero state response,
(c) Natural response,
(d) Forced response, and
(e) Total response.
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