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Method for constructing solutions of linear ordinary differential equations with constant coefficients

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Abstract

For Cauchy problems involving linear differential equations with constant coefficients, a new method for constructing solutions without determining the roots of the characteristic equation is proposed. Formulas for the differentiation of the solution with respect to the equation coefficients are derived, and an approximate analytical solution is found.

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Authors and Affiliations

  1. Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080, Russia

    V. V. Karachik

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  1. V. V. Karachik
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Correspondence to V. V. Karachik.

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Original Russian Text © V.V. Karachik, 2012, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2012, Vol. 52, No. 2, pp. 237–252.

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Karachik, V.V. Method for constructing solutions of linear ordinary differential equations with constant coefficients. Comput. Math. and Math. Phys. 52, 219–234 (2012). https://doi.org/10.1134/S0965542512020108

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  • DOI: https://doi.org/10.1134/S0965542512020108

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