\[ y'(x)=\frac {a x^2 F\left (\frac {a x y(x)+1}{a x}\right )+1}{a x^2} \] ✓ Mathematica : cpu = 20.6945 (sec), leaf count = 103
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {1}{F\left (K[2]+\frac {1}{a x}\right )}-\int _1^x \frac {F'\left (\frac {1}{a K[1]}+K[2]\right )}{a K[1]^2 F\left (\frac {1}{a K[1]}+K[2]\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x \left (-\frac {1}{a K[1]^2 F\left (\frac {1}{a K[1]}+y(x)\right )}-1\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 1.818 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) ax-1}{ax}} \right \} \]