,

where and with the following linear boundary conditions:

: periodic: , initial: , or final: ;

: periodic: , Dirichlet: or Neumann: ;

: periodic: ;

: periodic: , simply supported beam: , or clamped beam .

The solution of the boundary value problem (differential equation and boundary conditions) is given by .

In the code, the expression for the corresponding Green's function is given for an arbitrary interval .