Title: 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 $2n, n\geq 2,$ is proposed.