The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

We apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.