  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 solve the taylor approximated $O(x)$ DGLAP equations by Lagrange's auxiliary
method and $O(x^2)$ equation by Method of Separation of Variables and then show
that the two solutions obtained in each for $O(x)$ and $O(x^2)$ are not
identical in general.Analysis of the results obtained are done in the range of
the recent HERA data.
