Linear ordinary differential equations: revisiting the impulsive response method using factorization

Abstract. We present an approach to the impulsive response method for solving linear ordinary differential equations based on the factorization of the differential operator. In the case of constant coefficients this approach avoids the following more advanced methods: distribution theory, Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is dealt with using the result of Mammana about the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients. 1.

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