Algorithms to determine solvability of linear integro-differential equations with analytic functions

Applying the method of power series to linear integro-differential equations yields vast infinite systems of linear algebraic equations for coefficients of these series. If the equation contains some members then it is practically impossible to construct such system and make a definite conclusion. As some initial equations of such systems differ from others, we proposed to use computer for their suitable presentation. Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.