Math — Calculus of Variations
The Euler-Lagrange equation for a functional.
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J[y] = \int_a^b L(x, y, y')\,dx
\frac{\partial L}{\partial y} - \frac{d}{dx}\frac{\partial L}{\partial y'} = 0
\text{Beltrami identity: } L - y'\frac{\partial L}{\partial y'} = C