The Normal System of Simultaneous Differential Equations

Abstract

We found in the L-transformation a superior tool for the solution of the initial value problem involving a single differential equation of n th order, when compared with the classical method. This was due to the fact that with the latter one has to adapt the derived solution to the specified initial values, while with the former this is accomplished automatically in the process of solution. In the course of adapting the solution in the classical method, one has to solve a system of n simultaneous linear equations in n unknowns — a time-consuming task, particularly for n > 3. This favourable characteristic of the Laplace transformation is particularly appreciated when solving initial value problems that involve systems of N simultaneous linear differential equations in N unknown functions. Indeed, the Laplace transformation provides the only practical method of solution of such problems for N > 2, requiring a tolerable amount of calculation.