A method is suggested for constructing a solution of the homogeneous integral equation of a three-dimensional, covariant, simultaneous theory of bound states formulated in a relativistic configurational representation. The method is based on representing the unknown solutions in the form of a combination of functions that includes hyperbolic functions and polynomials (degenerate power series). Using this method and the REDUCE system of analytical calculations, the exact conditions determining the mass spectrum and the exact wave functions for a two-particle relativistic system with a quasi-potential [tanh(πr/2)]/r are found.