  Ten new exact solutions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$
are presented. The solutions are obtained by assuming certain relations among
the coefficients $a(x)$, $b(x)$ and $c(x)$ of the Riccati equation, in the form
of some integral or differential expressions, also involving some arbitrary
functions. By appropriately choosing the form of the coefficients of the
Riccati equation, with the help of the conditions imposed on the coefficients,
we obtain ten new integrability cases for the Riccati equation. For each case
the general solution of the Riccati equation is also presented. The possibility
of the application of the obtained mathematical results for the study of
anisotropic general relativistic stellar models is also briefly considered.
