\[ y'(x)=\frac {2 a}{x^2 \left (2 a F\left (\frac {x y(x)^2-4 a}{x}\right )-y(x)\right )} \] ✓ Mathematica : cpu = 32.8748 (sec), leaf count = 127
\[\text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \frac {2 K[2] F'\left (\frac {K[1] K[2]^2-4 a}{K[1]}\right )}{K[1]^2 F\left (\frac {K[1] K[2]^2-4 a}{K[1]}\right )^2} \, dK[1]-\frac {K[2]}{2 a F\left (\frac {x K[2]^2-4 a}{x}\right )}+1\right ) \, dK[2]+\int _1^x -\frac {1}{K[1]^2 F\left (\frac {y(x)^2 K[1]-4 a}{K[1]}\right )} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.409 (sec), leaf count = 37
\[ \left \{ -{\frac {y \left ( x \right ) }{2\,a}}+{\frac {1}{8\,{a}^{2}}\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,{\frac {a}{x}}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}-{\it \_C1}=0 \right \} \]