\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{a{x}^{2}} \left ( 1+F \left ( {\frac {axy \left ( x \right ) +1}{ax}} \right ) a{x}^{2} \right ) }=0} \]
Mathematica: cpu = 16.699621 (sec), leaf count = 139 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {F\left (\frac {a x K[2]+1}{a x}\right ) \int _1^x \frac {F'\left (\frac {a K[1] K[2]+1}{a K[1]}\right )}{a K[1]^2 F\left (\frac {a K[1] K[2]+1}{a K[1]}\right )^2} \, dK[1]-1}{F\left (\frac {a x K[2]+1}{a x}\right )} \, dK[2]+\int _1^x \left (-\frac {1}{a K[1]^2 F\left (\frac {a y(x) K[1]+1}{a K[1]}\right )}-1\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.156 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{ \it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a }}+{\it \_C1} \right ) ax-1}{ax}} \right \} \]