Reduction of an nth-order equation to a first-order system (Q1991)

y^{(n)}=f(x,y,y',\\ldots,y^{(n-1)})\\ \\Longrightarrow\\ y_1=y,\\; y_2=y',\\;\\ldots,\\;y_n=y^{(n-1)},\\qquad \\begin{cases} y_1'=y_2 \\\\ y_2'=y_3 \\\\ \\vdots \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases}