\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a}{{x}^{2}} \left ( -y \left ( x \right ) +2\,F \left ( {\frac {x \left ( y \left ( x \right ) \right ) ^{2}-4\,a}{x}} \right ) a \right ) ^{-1}}=0} \]
Mathematica: cpu = 27.163949 (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 = 0.296 (sec), leaf count = 37 \[ \left \{ -{\frac {y \left ( x \right ) }{2\,a}}+{\frac {1}{8\,{a}^{2}} \int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,{\frac {a}{x}}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}-{\it \_C1}=0 \right \} \]