Reduction of order for ordinary differential equations (Q1991)

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