Solution:

An example of the class of linear constant-coefficient difference equations is the accumulator system defined by,

$$ y[n]=\sum_{k=-\infty}^n x[k]....(1) . $$

To show that the input and output satisfy a differential equation, note that we can write the output for $n-1$ as

$$ y[n-1]=\sum_{k=-\infty}^{n-1} x[k]....(2) $$

By separating the …