Euler-Lagrange equation

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Euler-Lagrange equation

[¦ȯi·lər lə′grānj i‚kwā·zhən]
(mathematics)
A partial differential equation arising in the calculus of variations, which provides a necessary condition that y (x) minimize the integral over some finite interval of f (x,y,y ′) dx, where y ′ = dy/dx; the equation is (δƒ(x,y,y ′)/δ y) - (d/dx)(δƒ(x,y,y ′)/δ y ′) =0. Also known as Euler's equation.