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.