Generic form

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: $$u(t) = (u^{(0)}(t),u^{(1)}(t),\ldots,u^{(m-1)}(t))$$ $$\begin{align*} f(u, t) = ( & f^{(0)}(u^{(0)},\ldots,u^{(m-1)})\\ & f^{(1)}(u^{(0)},\ldots,u^{(m-1)}),\\ & \vdots\\ & f^{(m-1)}(u^{(0)}(t),\ldots,u^{(m-1)}(t))) \end{align*}$$