Building a basis for one-dimensional boundary-value problems in systems of symbolic computations

Discussed the possibility of using the Maple system of symbolic calculations to build a basis of coordinate functions, satisfying homogeneous boundary conditions, in the study of boundary value problems approximate analytical methods - Ritz or Bubnov-Galerkin. Examples of constructing a basis for the operators of the second and fourth orders. Discussed the possibility of orthogonalization of the basis for the energy operator and the construction of the green’s function in the system Maple.