Search

A method for finding solutions of the Riccati differential equation $y' = P(x) + Q(x)y + R(x)y^2$ is introduced. Provided that certain relations exist between the coefficient $P(x)$, $Q(x)$ and $R(x)$, the above equation can be solved in closed form. We determine the required relations and find the general solutions to the aforementioned equation. The method is then applied to the Riccati equation arising in the solution of the multidimensional Gross-Pitaevskii equation of Bose-Einstein condensates by the F-expansion and the balance principle techniques.