\[ y'(x)=\frac {2 y(x)^3}{2 y(x) F\left (\frac {4 x y(x)^2+1}{y(x)^2}\right )+1} \] ✓ Mathematica : cpu = 29.325 (sec), leaf count = 97
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {\frac {1}{F\left (\frac {1}{K[2]^2}+4 x\right )}+2 K[2]}{2 K[2]^3}-\int _1^x -\frac {2 F'\left (4 K[1]+\frac {1}{K[2]^2}\right )}{K[2]^3 F\left (4 K[1]+\frac {1}{K[2]^2}\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x -\frac {1}{F\left (4 K[1]+\frac {1}{y(x)^2}\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.163 (sec), leaf count = 30
\[ \left \{ -{\it \_C1}- \left ( y \left ( x \right ) \right ) ^{-1}-{\frac {\int ^{4\,x+ \left ( y \left ( x \right ) \right ) ^{-2}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{4}}=0 \right \} \]