<p>An inhomogeneous mixed parabolic–hyperbolic equation of second order is considered in the rectangular domain. We find a solution to the Dezin problem for the above equation satisfying the internal boundary condition linking the desired function on the line of change of the equation type with the normal derivative on the boundary in the domain of hyperbolicity and inhomogeneous boundary condition of the second kind. The substitution performed allows to reduce the problem to an equivalent one and, without loss of generality, to a problem with homogeneous conditions for a non-homogeneous equation. The proofs for the theorems of uniqueness and existence are obtained, and the solution is written out in an explicit form.</p>