\[ y'(x)=\frac {2 a}{2 a F\left (y(x)^2-4 a x\right )+y(x)} \] ✓ Mathematica : cpu = 23.9055 (sec), leaf count = 108
\[\text {Solve}\left [c_1=\int _1^{y(x)} \frac {1}{4} \left (\frac {\frac {K[2]}{F\left (K[2]^2-4 a x\right )}+2 a}{a^2}-4 \int _1^x \frac {K[2] F'\left (K[2]^2-4 a K[1]\right )}{a F\left (K[2]^2-4 a K[1]\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x -\frac {1}{2 a F\left (y(x)^2-4 a K[1]\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 5.504 (sec), leaf count = 35
\[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}+{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{8\,{a}^{2}}}-{\it \_C1}=0 \right \} \]