Riccati Equation: existence/uniqueness relation

What does the existence/uniqueness theorem say about solutions to initial value problems for Riccati equations of the form

http://www.mathhelpforum.com/math-he...24257514-1.gif

This is what I came up with, but I'm not sure.

A Riccati Equation of a particular form has a unique solution satisfies the following conditions:

It is to exist for large values of the independent variable

Its graph must stay above a certain line for large values of *the variable*