Use the \(\mathcal{Z}\)-transform to solve the difference equation

\[y(k)-3 y(k-1)+2 y(k-2)=2 u(k-1)-2 u(k-2)\]

where

\[\begin{aligned}u(k) & =k, \quad k \geq 0 \\& =0, \quad k<0 \\y(k) & =0, \quad k>0 .\end{aligned}\]