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

F\\bigl(x,y,y',y'',\\ldots,y^{(n)}\\bigr)=0 \\Longrightarrow \\begin{cases} y_1'=y_2 \\\\ y_2'=y_3 \\\\ \\vdots \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases}