Analytical Integral Solution of Inverse Lagrangian Problems via Heaviside Operational Schemes

In this brief note, a relatively straight-forward method for exact integral solution of ILP [Inverse Lagrangian Problems] is presented. An exact quadrature solution (i.e., Lagrangian) of the Inhomogeneous Lagrange Equation [ILE] is constructed for given inhomogeneous term of arbitrary dependence upon its arguments, via Heaviside operational schemes. Thus an inverse ILE problem is solved: a Lagrangian obtains in the form of an integral of the arbitrarily prescribed inhomogeneous term.