The Jacobi last multiplier, Lagrangian and Hamiltonian for Levinson-Smith type equations

We derive the Jacobi last multiplier for second-order ordinary differential equations of the Levinson-Smith type by using a combination of previous techniques employed for the Liénard-I and II classes of equations. This opens up the possibility for a Lagrangian or Hamiltonian description of the systems governed by the Levinson-Smith type of equations as well as simplifying the problem of finding first integrals of motion. The procedure has been illustrated by a number of suitable examples alongwith Kamke's equation with explicit time dependent coefficients.