We investigate the effectiveness of Differential Transform Method (DTM) for a hydrodynamically fully developed flow of Newtonian fluid actuated by electroosmotic force and pressure gradient in a microchannel with parallel plates influenced by a magnetic field. Expressions are derived for velocity as well as flow rate in dimensionless form via DTM and analytical methods and the convergence rate of the former has been computed by maximum relative percentage deviation. For lower values of Hartmann number, there is flow velocity augmentation whereas trend reversal prevails for comparatively higher values of the same. Critical values of Hartmann number and dimensionless transverse electric field have been obtained beyond which employing DTM gives highly efficient and convergent solutions with minimal percentage deviation for flow velocity. Flow rate augmentation is observed with enhanced transverse electric field and lower values of Hartmann number.