Reduction of order for ordinary differential equations (Q1991)

F\\bigl(x,y,y',y'',\\ldots,y^{(n)}\\bigr)=0 \\Longrightarrow \\begin{cases} y_2=y_1' \\\\ y_3=y_2' \\\\ \\vdots \\\\ y_n=y_{n-1}' \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases}