Solutions of a class of Duffing oscillators with variable coefficients (Q649924)

Using the factorization technique, the solutions of an ODE with a cubic term and variable coefficients of the form \[ Y_{tt}(t)+F_1(t)Y_t(t)+2F_2^2(t)Y^3(t)+F_3(t)Y(t)+F_4(t)=0 \] are obtained explicitly. The Lagrangian, the Hamiltonian and the constant of the motion are also found. The results are exemplified on a damped and forced pendulum example.