Systems of ODEs

An nxn system of ODEs looks like the following

${\begin{aligned}x_{1}'&=F_{1}(t,x_{1},x_{2},\ldots ,x_{n})\\x_{2}'&=F_{2}(t,x_{1},x_{2},\ldots ,x_{n})\\\ldots \\x_{n}'&=F_{n}(t,x_{1},x_{2},\ldots ,x_{n})\\\end{aligned}}$

In vector form, the same equation can be written as

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{x}'=\vec{F}(t,\vec{x}) }

Non-linear ODEs are very complicated (like chaos theory, three body problem, etc.)