\[ y'(x)=\frac {2 a}{2 a F\left (y(x)^2-4 a x\right )+y(x)} \] ✓ Mathematica : cpu = 0.284573 (sec), leaf count = 115
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{4 a^2 F\left (K[2]^2-4 a x\right )}-\frac {2 a \int _1^x\frac {K[2] F'\left (K[2]^2-4 a K[1]\right )}{a F\left (K[2]^2-4 a K[1]\right )^2}dK[1]-1}{2 a}\right )dK[2]+\int _1^x-\frac {1}{2 a F\left (y(x)^2-4 a K[1]\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.244 (sec), leaf count = 35
\[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}+{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{8\,{a}^{2}}}-{\it \_C1}=0 \right \} \]