New Conditions for Obtaining the Exact Solutions of the General Riccati Equation

الملخص EN

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.