  Coupled DGLAP equations involving singlet quark and gluon distributions are
explored by a Taylor expansion as two first order partial differential
equations in two variables. The system of equations are then solved by the
Lagrange's method and Method of Characteristics. We obtain the proton structure
function by combining the corresponding non-singlet and singlet structure
functions by both the methods. Analytical solutions for proton structure
function thus obtained are compared with the data available and their
compatibility is checked. Data favors the analytical solution by Lagrange's
method.
