ABSTRACT
This chapter deals with second-order differential equations. It helps the reader able to recognize a second-order linear differential equation, write down the general solution in the homogeneous case, and use the method of trial solutions to obtain a particular solution in the non-homogeneous case. The chapter assists in anticipating the breakdown case and remedying the situation and solve a general linear second-order differential equation with constant coefficients. Any part of the solution x of a differential equation which tends to zero as the independent variable t tends to infinity is known as a transient. When t is large enough for the transients to be neglected, that which remains is known as the steady state. In this way we obtain the equation general solution = transient + steady state. The chapter also demonstrates how to solve practical problems in filtering, circuits and mechanical oscillations.
