Show that the second-order differential equation \(y″ = F(x, y, y′)\) can be reduced to a system of two first-order differential equations

\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={z},{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{x}\right.}}}}={F}{\left({x},{y},{z}\right)}.\)

Can something similar be done to the nth-order differential equation

\(\displaystyle{y}^{{{\left({n}\right)}}}={F}{\left({x},{y},{y}',{y}{''},\ldots,{y}^{{{\left({n}-{1}\right)}}}\right)}?\)