Lagrangian Representations and Solutions of Modified Emden-Type Equations

We derive two novel methods to construct solutions of the physically important modified Emden-type equations (MEEs). Following the basic philosophy implied in the Lagrange’s method of variation of parameters, we make use of a trivial particular solution of the problem to construct expressions for the nontrivial general solutions. Secondly, we judiciously adapt the factorization method of differential operators to present solutions of certain oscillator equations obtained by adding a linear term to the MEEs. We provide Lagrangian and Hamiltonian formulations of these equations in order to look for another useful theoretical model for solving MEEs.