The laplace transformation in the solution of differential equations with calculation algorithms in mathcad

Abstract

In the history of Mathematics, frequently happens that certain topics (especially the numeric calculation) has perfectly defined its theoretical solution, but the heap of operations to find a conclusive result, in multiple occasions, don’t allow to arrive to the final results. The solution of differential equations represents a demonstrative example. At the end of the XIX century, the electricity was a fundamental theme in the society and every time new situations appeared that complicates the solution of technical problems, especially with the theory of the electric circuits, where was necessary solving differential equations with classic methods, making intense use of the techniques of integration and derivation, which constituted, in multiple occasions, a remarkable obstacle from the engendering point of view, and it was at the end of the century when an English electrical engineer established a group of practical rules to arrive to this solutions without necessity of using the basics of calculus. Although these rules propitiated the solutions, was necessary to do complex algebraic operations, in occasions, long and tedious, so, comparatively, it was not clear which procedure would be the best. At the present time, with the support of mathematical software, especially Mathcad, we can arrive to this solution in a quick way and with a high grade of precision. In the present text is described an algorithmic procedure to find the solution of differential equations with initial conditions, applying the transformed of Laplace.

DOI: http://dx.doi.org/10.21017/rimci.2019.v6.n12.a64