Computer algorithm for solving of the Chazy equation of the third order with six singular points

The algorithm for calculating the coefficients of Chazy differential equation of the third order with six constant poles with respect to the unknown function is given. For such values of the poles a corresponding differential equation can be integrated in a symbolic form. When solving this problem the computational-algebraic algorithm to the construction of five non-linear differential equations of the third order, which are reduced to a linear inhomogeneous equations of the second order with six singular points is built. The algorithm is demonstrated on an example; five differential equations are obtained and their general solutions are found in elliptic functions. The calculations are implemented using Mathematica system.