  We use Vessiot theory and exterior calculus to solve partial differential
equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated
evolution equations. These equations are represented by the Vessiot
distribution of vector fields. We develop and apply an algorithm to find the
largest integrable sub-distributions and hence solutions of the PDEs. We then
apply the integrating factor technique [19] to integrate this integrable
Vessiot sub-distribution. The method is successfully applied to a large class
of linear and non-linear PDEs.
