How to find solutions, Lie symmetries, and conservation laws of forced Korteweg-de Vries equations in optimal way

It is shown that the forced Korteweg-de Vries (KdV) equation studied in the recent papers [A.H. Salas, Computing solutions to a forced KdV equation, Nonlinear Anal. RWA 12 (2011) 1314-1320] and [M.L. Gandarias, M.S. Bruzon, Some conservation laws for a forced KdV equation, Nonlinear Anal. RWA 13 (2012) 2692-2700] is reduced to the classical (constant-coefficient) KdV equation by point transformations for all values of variable coefficients. The equivalence-based approach proposed in [R.O. Popovych, O.O. Vaneeva, More common errors in finding exact solutions of nonlinear differential equations: part I, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 3887-3899] allows one to obtain more results in a much simpler way. (C) 2012 Elsevier Ltd. All rights reserved.