\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a}{y \left ( x \right ) +2\,F \left ( \left ( y \left ( x \right ) \right ) ^{2}-4\,ax \right ) a}}=0} \]
Mathematica: cpu = 18.981910 (sec), leaf count = 112 \[ \text {Solve}\left [\int _1^{y(x)} \left (\frac {K[2]}{4 a^2 F\left (K[2]^2-4 a x\right )}-\frac {2 a \int _1^x \frac {K[2] F'\left (K[2]^2-4 a K[1]\right )}{a F\left (K[2]^2-4 a K[1]\right )^2} \, dK[1]-1}{2 a}\right ) \, dK[2]+\int _1^x -\frac {1}{2 a F\left (y(x)^2-4 a K[1]\right )} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 35 \[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}+{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{8\,{a}^{2}}}-{\it \_C1}=0 \right \} \]