The Multiplier Problem of the Calculus of Variations for Scalar Ordinary Differential Equations
Abstract
In the inverse problem of the calculus of variations one is asked to find a Lagrangian and a multiplier so that a given differential equation, after multiplying with the multiplier, becomes the Euler--Lagrange equation for the Lagrangian. An answer to this problem for the case of a scalar ordinary differential equation of order 2n, n≥ 2, is proposed.
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