One case of solution in a closed form of Markushevich boundary problem for semiplane

In the article an explicit method for the solution of Markushevich boundary value problem directed by L. I. Chibrikova in the class of piecewise analytic functions is given. Boundary condition of the problem is given on the line. The problem is found in a closed form under certain constratints on the coefficient $b(t)$ of the problem.