ABSTRACT
This chapter focuses on the qualitative behaviour of the solution of a nonlinear second order differential equation in which the independent variable t does not appear in any of the coefficients of the equation. It discusses two autonomous systems: a problem in mechanics in the form and a problem in population dynamics in the form. A popular approach to a nonlinear differential equation is to ignore the nonlinear terms and to solve the resulting linear equation. The nonlinear initial value problem describes the motion of the simple pendulum, and so the construction stage of the mathematical model is settled. The chapter uses Newton's second law to construct a mathematical model of the motion of the bob. The nonlinear initial value problem describes the motion of the simple pendulum, and so the construction stage of the mathematical model is settled.
