  The first order nonlinear ODE \dot \phi(t) +
\sin\phi(t)=q(t),q(t)=B+A\cos\omega t, where A,B,\omega are real constants, is
considered, the transformation converting it to a second order linear
homogeneous ODE with polynoimial coefficients is found. The latter is
identified as a particular case of the double confluent Heun equation. The
series of algebraic constraints on the constant parameters is found whose
fulfillment leads to the existance of solutions representable through
polynomials in explicit form. These polynomials are found to constitute the
orthogonal normalizable system
