The electroosmotic flow plays an important role in electrokinetic phenomena, in particular, in the flow of an electrolyte solution in a microchannel, where the electrokinetic equations need to be solved. In general, these equations are coupled, nonlinear partial differential equations, and solving them analytically is nontrivial. In this study the electrokinetic equations are solved analytically for the case of a general electrolyte solution flow through a planar slit comprising two planar, parallel surfaces, which can have different charged conditions, and the influences of the key parameters on the flow behavior are discussed. Several interesting phenomena are observed. For example, the absolute value of the mean fluid velocity may exhibit an undulant behavior as the bulk concentration of counterions varies. Also, if both the valence of coions and the bulk concentration of counterions are fixed, then depending upon the level of the latter the absolute value of the mean fluid velocity may have a local maximum or local minimum as the valence of counterions varies.