How can I solve the differential equation $y'+y^{2}=f(x)$? $$y'+y^{2}=f(x)$$
I know how to find  endless series solution via  endless integral or endless derivatives and power series solution if we know $f(x)$. I also know how to find general solution if we know one particular solution ($y_0$).
I am looking for an exact analitic solution $y= L({f(x)})$ without knowing a particular solution,  if it exists. (Here $L$ defines an operator such as integral, derivative, radical, or any defined function.) If it does not exist, could you please prove why we cannot find it?
Note: This equation is related to second order differantial linear equation. If we put $y=u'/u$, this equation will turn into $u''(x)-f(x).u(x)=0$. If we the find general solution of $y'+y^{2}=f(x)$, it means that $u''(x)-f(x).u(x)=0$ will be solved as well. As we know, many functions such as Bessel function or Hermite polinoms and so many special functions are related to Second order linear differential equations.
Thank you for answers.
EDIT:
I asked the question in mathoverflow too. You can also find the link below for details.   (1-Endless transform, 2-Endless Integral,3-Endless Derivatives,4-Power series) and answers about the subject.
https://mathoverflow.net/questions/87041/looking-for-the-solution-of-first-order-non-linear-differential-equation-y-y

Interesting.  In Maple I tried $y'+y^2 = \sin(x)$, and the solution involves Mathieu functions $S, C, S', C'$.  
I tried $y'+y^2=x$, and the solution involves Airy functions Ai, Bi.  
I tried $y'+y^2=1/x$, and the solution involves Bessel functions $I_0, I_1, K_0, K_1$.  
This is a Riccati equation.  For more info, in particular how its solutions are related to solutions of a second-order linear equation, look that up.
