= System of ordinary differential equations
{title2=$\mathbf y'=\mathbf f(t,\mathbf y)$}
A system of ordinary differential equations specifies derivatives of several unknown <functions> of one independent variable. A vector-valued form $\mathbf y'=\mathbf f(t,\mathbf y)$ bundles its scalar equations. A scalar second-order <ordinary differential equation> $y''=F(t,y,y')$ becomes the first-order system $(y_1',y_2')=(y_2,F(t,y_1,y_2))$ by introducing position and velocity variables. Conversely the first equation identifies $y_2=y_1'$ and the second recovers the original equation. Its <initial condition> must specify both variables.
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