Algebraic analysis of oscillatory solutions in second order linear differential equations of with complex roots
DOI:
https://doi.org/10.62059/LatArXiv.preprints.350Keywords:
Differential equations, Complex roots, Oscillatory solutions, Algebraic analysis, Computational visualizationAbstract
This paper analyzes from an algebraic approach the solutions of second order homogeneous linear differential equations with constant coefficients, when the associated characteristic equation presents complex conjugate roots. It is shown that such solutions can be represented as linear combinations of sine and cosine functions multiplied by real exponentials. Fundamental properties of the solution space are established, such as linearity, independence and analytical behavior. The analysis is performed exclusively from a mathematical perspective, without resorting to graphical interpretations or physical applications.
References
Zill, D. G. (2014). Ecuaciones diferenciales con aplicaciones de modelado. Cengage Learning.
Boyce, W. E., & DiPrima, R. C. (2017). Ecuaciones diferenciales y problemas con valores en la frontera. Cengage Learning.
Simmons, G. F. (1991). Differential Equations with Applications and Historical Notes. McGraw-Hill.
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Data Availability Statement
Él autor no han generado ni utilizado conjuntos de datos en esta investigación, por lo que no se dispone de datos para compartir.
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Copyright (c) 2025 Andres Felipe Orduz Perez (Autor/a)
This work is licensed under a Creative Commons Attribution 4.0 International License.
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