  In 1890 German mathematician and physicist W. Hess found new special case of
integrability of Euler - Poisson equations of motion of a heavy rigid body with
a fixed point. In 1892 P. A. Nekrasov proved that the solution of the problem
of motion of a heavy rigid body with a fixed point under Hess conditions
reduces to integrating the second order linear differential equation. In this
paper the corresponding linear differential equation is derived and its
coefficients are presented in the rational form. Using the Kovacic algorithm,
we proved that the liouvillian solutions of the corresponding second order
linear differential equation exists only in the case, when the moving rigid
body is the Lagrange top, or in the case when the constant of the area integral
is zero.
