First-order ordinary differential equation (source code)

= First-order ordinary differential equation
{title2=$y'=F(x,y)$}

A first-order <ordinary differential equation> contains the first <derivative> of its unknown function and no higher derivative. When solved for that derivative it has the displayed form. With an initial condition, local existence and uniqueness follow under appropriate regularity assumptions on $F$; the order alone does not guarantee either property.