I have been working on Riccati Equation. I have tried many different methods to find a closed form for the solution of first order non-linear differential equation ($y'+y^{2}=f(x)$) without knowing a particular solution. My aim is to open a topic and to collect all known methods and to progress finding the general solution of Ricatti Equation without knowing a particular solution (if possible). May be it can be proved that the solution cannot be expressed in closed form. Actually, I am looking for a similar closed form to linear differential equation ( $y'+y=f(x) $) as known $y=e^{-x}\int{f(x)e^{x}}dx $

I have been working on Riccati Equation. I have tried many different methods to find a closed form for the solution of first order non-linear differential equation ($y'+y^{2}=f(x)$) without knowing a particular solution. My aim is to open a topic and to collect all known methods and to progress finding the general solution of Riccati Equation without knowing a particular solution (if possible). May be it can be proved that the solution cannot be expressed in closed form. Actually, I am looking for a similar closed form to linear differential equation ( $y'+y=f(x) $) as known $y=e^{-x}\int{f(x)e^{x}}dx $

Note:I asked the same question in math.stackexchange.com and I noticed that also theories can be asked here. I decided to open a topic here too you can see the link ( http://math.stackexchange.com/questions/99850/how-can-i-solve-the-differential-equation-yy2-fx )

Note:I asked the same question in math.stackexchange.com and I noticed that also theories can be asked here. I decided to open a topic here too you can see the link ( https://math.stackexchange.com/questions/99850/how-can-i-solve-the-differential-equation-yy2-fx )

I have been working on Riccati Equation. I have tried many different methods to find a closed form for the solution of one order non-linear differential equation ($y'+y^{2}=f(x)$) without knowing a particular solution. My aim is to open a topic and to collect all known methods and to progress to find a general solution of Ricatti Equation without knowing a particular solution (if possible). May be it can be proved that the solution cannot be expressed in closed form. Actually, I am looking for a similar closed form to linear differential equation ( $y'+y=f(x) $) as known $y=e^{-x}\int{f(x)e^{x}}dx $

I have been working on Riccati Equation. I have tried many different methods to find a closed form for the solution of first order non-linear differential equation ($y'+y^{2}=f(x)$) without knowing a particular solution. My aim is to open a topic and to collect all known methods and to progress finding the general solution of Ricatti Equation without knowing a particular solution (if possible). May be it can be proved that the solution cannot be expressed in closed form. Actually, I am looking for a similar closed form to linear differential equation ( $y'+y=f(x) $) as known $y=e^{-x}\int{f(x)e^{x}}dx $