On inverse problem for an ordinary differential equation

The inverse problem for an ordinary linear differential equation of the n-th order consists in constructing approximation to the right side of the equation given an approximate solution of the boundary problem of general form. This problem is being reduced to the problem of constructing uniform approximations of a function together with its derivatives up to the $n$-th order from the domain of definition of an arbitrary differential operator. The error of an approximate solution is estimated.