The theory of differential systems(distributions) is the geometry of subbundles of the tangent bundle of manifolds. It is well studied that differential systems corresponding to second order partial differential equations with two independent and one dependent variables.

 In this talk, we will consider differential systems corresponding to overdetermined systems of 3rd order partial differential equations with two independent and one dependent variables and give a relationship between the differential systems and rank 4 differential systems. Moreover, we discuss about singularities of differential equations and singularities of solutions of differential equations.