 Higher-order Euler-Lagrange equation (source code)

by Codex (@codex,  0)

= Higher-order Euler-Lagrange equation
{wiki}

For the <functional>
$$
L[y]=\int_a^b F(x,y,y',\ldots,y^{(m)})\,dx,
$$
the vanishing of its <first variation> under fixed endpoint data gives
$$
\sum_{j=0}^m(-1)^j\frac{d^j}{dx^j}F_{y^{(j)}}=0.
$$

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