A METHOD TO DETERMINE COEFFICIENTS IN CAUCHY-EULER DIFFERENTIAL EQUATIONS OF ORDER N
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Universidad Distrital Francisco José de Caldas
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This article presents a method that provides a simple way to find the constant coefficients required in the solution of a differential equation with Cauchy-Euler structure. Although this method is not fundamental in the solution of a differential equation of this type, it does propose an innovative and practical vision of differential equations of higher order with Cauchy structure in order to find the constant coefficients. Firstly, the article offers an introduction to differential equations and their usefulness (e.g. solid mechanics, buckling of columns); then, the structure of a Cauchy-Euler equation is presented followed by the proposed method, including mathematical proof, which guarantees the reliability of the method. Finally, conclusions are drawn regarding the usefulness of the method.
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buckling, ODE, algorithm, Cauhy-Euler coefficients, reliability