$fx(1-x)y'+(e+fx)y+\sqrt{ay-b}=dx+c$, where $y=y(x)$
EDIT, Will Jagy: $a,b,c,d,e,f$ are real constants.
I have never solved a nonlinear ODE before, although I'm familiar with many of the techniques applied for solving linear ODEs. There is one special case of the equation above that I managed to solve, but that is the easy case where $f$ is equal to zero. For $f$ not being equal to zero I have the first derivative inside, which then makes it a linear ODE. I read that there does not have to be a closed form solution. Is there any way how I can check whether or not such a solution exists for the equation above?