= Second-order differential equation
{title2=$y''=f(x,y,y')$}
A second-order <ordinary differential equation> involves a second <derivative> as its highest derivative. In explicit form $y''=f(x,y,y')$, introducing $v=y'$ converts it into the first-order system $y'=v$, $v'=f(x,y,v)$. Under local regularity and <Lipschitz continuity> in the dependent variables, an <initial value problem> is specified by both $y(x_0)$ and $y'(x_0)$. The linear case is a <second-order linear differential equation>.
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