title: New conditions for obtaining the exact solutions of the general Riccati equation.
abstract: We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.
authors.affiliation: Department of Mathematics, Faculty of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia.
authors.forename: Lazhar
authors.initials: L
authors.lastname: Bougoffa
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical