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The standard form for ODEs: $$ \begin{equation} u' = f(u,t),\quad u(0)=I \tag{37} \end{equation} $$
\( u \) and \( f \): scalar or vector.
Vectors in case of ODE systems: $$ u(t) = (u^{(0)}(t),u^{(1)}(t),\ldots,u^{(m-1)}(t)) $$ $$ \begin{align*} f(u, t) = ( & f^{(0)}(u^{(0)},\ldots,u^{(m-1)})\\ & f^{(1)}(u^{(0)},\ldots,u^{(m-1)}),\\ & \vdots\\ & f^{(m-1)}(u^{(0)}(t),\ldots,u^{(m-1)}(t))) \end{align*} $$
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