A boundary value problem for integro-differential equation is considered. The method proposed by
D.S. Dzhumabaev for solving this problem is described and its results are commented. A new general solution of integrodifferential
equations is constructed and its properties are established. Algorithms for finding solutions to the boundary
value problems for integro-differential equations are constructed and conditions for unique solvability are established in
the terms of initial data. The results are illustrated by examples.