Abstract
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the n th-order homogeneous linear differential equation with constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp [At]. We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than, the other methods.
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References
Putzer, J., Avoiding the Jordan canonical form in the discussion of linear systems with constant coefficients.The American Mathematical Monthly,73, 1 (1966).
Iooss, G. and D. D. Joseph, Elementary Stability and Bifurcation Theory, New York, Springer (1980), 46–57.
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Yong-nian, H. The explicit solution of homogeneous linear oridinary differential equations with constant coefficients. Appl Math Mech 13, 1115–1120 (1992). https://doi.org/10.1007/BF02456151
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DOI: https://doi.org/10.1007/BF02456151