ABSTRACT

The general solution of a linear differential equation [1,2] is the sum of two components, the particular integral and the complementary function. Often the particular integral is the steadystate component of the solution of the differential equation; the complementary function, which is the solution of the corresponding homogeneous equation, is then the transient component of the solution. Often the steady-state component of the response has the same form as the driving function. In this book the particular integral is called the steady-state solution even when it is not periodic. The form of the transient component of the response depends only on the roots of the characteristic equation. For nonlinear differential equations, the form of the response also depends on the initial or boundary conditions. The instantaneous value of the transient component depends on the boundary conditions, the roots of the characteristic equation, and the instantaneous value of the steady-state component.