  The authors proposed a general way to find particular solutions for
overdetermined systems of PDEs previously, where the number of equations is
greater than the number of unknown functions. In this paper, we propose an
algorithm for finding solutions for overdetermined PDE systems, where we use a
method for finding an explicit solution for overdetermined algebraic
(polynomial) equations. Using this algorithm, the solution of some
overdetermined PDE systems can be obtained in explicit form. The main
difficulty of this algorithm is the huge number of polynomial equations that
arise, which need to be investigated and solved numerically or explicitly. For
example, the overdetermined hydrodynamic equations obtained earlier by the
authors give a minimum of 10 million such equations. However, if they are
solved explicitly, then we can write out the solution of the hydrodynamic
equations in a general form, which is of great scientific interest.
