  The current paper is the second part of a series of two papers dedicated to
2D problem of diffraction of acoustic waves by a segment bearing impedance
boundary conditions. In the first part some preliminary steps were made,
namely, the problem was reduced to two matrix Riemann-Hilbert problem. Here the
Riemann-Hilbert problems are solved with the help of a novel method of
OE-equations.
  Each Riemann-Hilbert problem is embedded into a family of similar problems
with the same coefficient and growth condition, but with some other cuts. The
family is indexed by an artificial parameter. It is proven that the dependence
of the solution on this parameter can be described by a simple ordinary
differential equation (ODE1). The boundary conditions for this equation are
known and the inverse problem of reconstruction of the coefficient of ODE1 from
the boundary conditions is formulated. This problem is called the OE-equation.
The OE-equation is solved by a simple numerical algorithm.
