Abstract In the article, a new method for finding of the analytical solution of a second-order ordinary differential equation with constant coefficients within a non-local boundary condition is proposed. Using the second Green formula, the fundamental relations are obtained, through which the necessary conditions for correctness of the problem are found. On the received fundamental relations for the arbitrary solution of the equation, the values for the solution at boundary points are obtained.
Si̇nsoysal et al. (2026) studied this question.