We obtain a pair of second order differential equations in two variables $x$ and $t$ from the coupled DGLAP QCD evolution equations at small $x$ using the standard Taylor series expansion method.To that end we keep terms upto $O(x^2)$.We use the standard assumption about the relationship between the singlet Structure Function and the gluon distributions available in current literature. We then show that the two solutions are not identical in general.Analysis of the results obtained are done in the range of the recent HERA data.We also study the limiting behaviour of our results taking only $O(x)$ and neglecting the $O(x^2)$.We also explore the corresponding solutions of dDGLAP equations as double parton interactions at LHC.