An autoresonance electron acceleration phenomenon in the combined steady-state inhomogeneous magnetic and microwave fields is analytically studied. Equations describing the evolution of the phase shift between the particle velocity and the microwave electric field, total energy, and longitudinal velocity of the electron are obtained. Linear and parabolic profiles of the magnetic field are examined. It is shown that the proper choice of the magnetic heterogeneity degree, the microwave electric field value, and initial electron velocity can retain the electron in the acceleration phase band. The results obtained in this work show a complete agreement with our previous autoresonance results obtained through simulations of the relativistic Newton-Lorentz equation.