The Method of Equivalent Lagrangians is used to find the solutions of a given
differential equation by exploiting the possible existence of an isomorphic Lie
point symmetry algebra and, more particularly, an isomorphic Noether point
symmetry algebra. Applications include ordinary differential equations such
as the Kummer Equation and the Combined Gravity-Inertial-Rossby Wave
Equation and certain classes of partial differential equations related to the
(1 + 1) linear wave equation. We also make generalisations to the (2 + 1) and
(3 + 1) linear wave equations.
