This paper describes an analytical solution of the exact equation for coherence function for parabolic profiles of the refractive index and amplification coefficient distribution in an active medium cross-section. The applicability limits of the radiation transfer equation are analyzed by a direct comparison of analytical solutions of the equation for coherence function and the radiation transfer equation for a wide range of the active medium dimensionless parameters. The problem of the applicability limits is also discussed based on a comparative analysis of general solutions of the exact and approximate integral equations.