The solution of a set of m ordinary linear differential equations of the nth order having variable coefficients can be provided by the use of a set of m2 indicial admittances and the solution is derived from that given by the use of impulsive admittances. The indicial admittances are easily derived from the impulsive admittances and vice versa.

An “indicial admittance” is a function representing the response of a system to an applied “input” in the form of a “unit step function” and the concept is due to Heaviside. When the indicial admittance is known, the response to an input which varies with time in an arbitrary manner can easily be found. Similarly, the response can easily be found when the “impulsive admittance” is known, where this is the response to a unit instantaneous impulsive input.