Given the difference equation

\[
x(k+3)-2.2 x(k+2)+1.57 x(k+1)-0.36 x(k)=e(k)
\]

where \(e(k)=1\) for all \(k \geq 0\), and \(x(0)=x(1)=x(2)=0\).

(a) Write a digital computer program that will calculate \(x(k)\). Run this program solving for \(x(3), x(4), \ldots\), \(x(25)\).

(b) Using the sequential technique, check the values of \(x(k), 0 \leq k \leq 5\).

(c) Use the \(z\)-transform and the power-series method to verify the values \(x(k), 0 \leq k \leq 5\).