  A new integrability condition of the Riccati equation
$dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation
depending on a generating function $f(x)$, the general solution of the Riccati
equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the
function $f(x)$ satisfy a particular constraint. The validity and reliability
of the method are tested by obtaining the general solutions of some Riccati
type differential equations. Some applications of the integrability conditions
for the case of the damped harmonic oscillator with time dependent frequency,
and for solitonic wave, are briefly discussed.
