How to solve the Riccati's differential equation I found this question in a differential equation textbook as a question
The equation
 $$             
               \frac{dy}{dx} =A(x)y^2 + B(x)y +C(x)
$$
is called Riccati's equation
show that if $f$ is any solution of the equation, then the transformation 
$$
                       y = f + \frac{1}{v}
$$
reduces it to a linear equation in $v$.
I am not understanding this, what does $f$ mean? How can we find the solution with the help of the solution itself. I hope anyone could help me to solve this differential equation. 

The question is wrongly posed, which is probably why you don't comprehend it. Here's the correct one: 
Let $y$ and $f$ be solutions to the above diff. equation such that $y=f+1/v$ for some function $v(x)$. Show that $v$ satisfies a linear diff. equation.
The solution is provided by Amzoti. 
