In this memory-analytical solutions are built with digital readouts of a priori error problems associated with mixed partial derivative equations with separable coefficients and conditions of Dirichlet type contour. By truncation strategies of formal solutions in series, and methods involved in multi autofunciones, analytical approximations are constructed with a numerical error in a predetermined domain bounded. The equation of diffusion of waves and the telegraph were treated with variable coefficients. The uniqueness of each problem is analyzed