|Revista Colombiana de Matemáticas|
Abstract. A method to find the general solution of algebraic equations, including the quintic, is presented. The procedure is essentially based on the analytical properties of the algebraic functions and leads to the solution of certain linear differential equations that these functions must satisfy.Palabras claves. Tschrinhaus transformation, discriminant of a polynomial, entire function, branch and algebraic branch point, generalized hypergeometric functions.