A vector field $V = \xi(x,u)\,\partial/\partial x + \eta(x,u)\,\partial/\partial u$ generates a Lie point symmetry of the ODE $u^{(n)} = \omega(x, u, u', \ldots, u^{(n-1)})$ if and only if \begin{align*} \mathrm{pr}^{(n)} V\bigl(u^{(n)} - \omega\bigr) = 0 \end{align*} whenever $u^{(n)} = \omega$ (i.e. on solutions of the ODE).