A common error and a better use of the Laplace transform

The advantage of using the Laplace transform in circuits and systems, mainly to solve systems of integral-differential equations, is weakened when the circuits or the systems have nonzero initial conditions to be taken into account. This is the result of using initial conditions in the Laplace transform of the derivative of the signal. The signals must have null initial conditions. The advantage of using the Laplace transform to find the solution of differential equations with initial conditions is not lost if the origin of time is shifted to the left or if the superposability property is used