The paper considers a boundary value problem for a third order with constant coefficients and normal derivatives. Odds. This is because introduces the concept of the conjugate Green's function. It is tough to write the form of the conjugate differential operator based on the Lagrange equation. Therefore, in this work, using boundary conditions under value boundary problems conditions and conjugate, an explicit form is found as a conjugate operator since the boundary value problem for integral-differential equations has been studied based on introducing conjugate for third-order differential equation systems. In this article, it can be said that Green's function is considered based on Lagrange's formula for the third-order differential equation with boundary conditions and its conjugate.