\[ y'(x)=\frac {a x^2 F\left (\frac {a x y(x)+1}{a x}\right )+1}{a x^2} \] ✓ Mathematica : cpu = 0.258947 (sec), leaf count = 142
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (\frac {a x K[2]+1}{a x}\right ) \int _1^x\frac {F'\left (\frac {a K[1] K[2]+1}{a K[1]}\right )}{a F\left (\frac {a K[1] K[2]+1}{a K[1]}\right )^2 K[1]^2}dK[1]-1}{F\left (\frac {a x K[2]+1}{a x}\right )}dK[2]+\int _1^x\left (-1-\frac {1}{a K[1]^2 F\left (\frac {a K[1] y(x)+1}{a K[1]}\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.28 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) ax-1}{ax}} \right \} \]