The Generalized Response of Linear Systems for Arbitrary Initial Conditions

A method is presented for the solution of ordinary linear differential equations with constant coefficients. This method stays wholly in the time domain and obtains a general solution in a compact form including the effects of initial conditions. The differential equation as treated involves a driving function made up of the sum of terms involving the system input and its derivatives. The general solution is also given in terms of weighting functions operating on the input (in the driving function) and including outside the weighted integral, terms involving initial conditions of the input as well as the dependent variable.