Associated fundamental matrices, Cauchy functions and wronskians of linear differential equations of the second order with generalized coefficients in the algebra of mnemofunctions

In the paper Cauchy problems for a homogeneous and nonhomogeneous linear differential equations with generalized coefficients in algebra mnemofunctions are investigated. Associated Cauchy functions and associated Wronskians are introduced and studied. Expressions for the Cauchy functions and for the fundamental matrices are found by the fundamental system of solutions. Representations associated solutions of the Cauchy problem are given by means of Cauchy functions.