ABSTRACT
The method transforms an ODE to an algebraic equation in the Laplace domain that can be manipulated into a form such that the inverse transform can be obtained from tables. The inverse transform is the solution to the differential equation. The inverse transform can also be obtained by residue theory in complex variables (which is beyond the scope of this textbook). The method is applicable to problems where the independent variable domain is from (0 to ∞). The method is particularly useful for linear, nonhomogeneous differential equations, such as vibration problems where the forcing function is piecewise continuous. In electrical engineering, the method is often used to solve circuit problems containing capacitors or inductors that contain at least one differential relationship.
