The Beltrami identity, named after Eugenio Beltrami, is a simplified and less general version of the Euler–Lagrange equation in the calculus of variations. The Euler–Lagrange equation serves to extremize action functionals of the form where a, b are constants and u′(x) = du / dx. For the special case of ∂L / ∂x = 0, the Euler–Lagrange equation reduces to the Beltrami identity, where C is a constant.