First Order Systems. Equations of Higher Order

Systems of Differential Equations.Direction Fields. By a first order system of differential equations (in explicit form) we mean a set of simultaneous equations of the form $$ \begin{array}{*{20}{c}} {{{y'}_1}}& = &{{f_1}\left( {x,{y_1}, \ldots ,{y_n}} \right)} \\ \vdots &{}& \vdots \\ {{{y'}_n}}& = &{{f_n}\left( {x,{y_1}, \ldots ,{y_n}} \right)} \end{array} $$ (1) .