\[ y'(x)=\frac {2 y(x)^3}{2 y(x) F\left (\frac {4 x y(x)^2+1}{y(x)^2}\right )+1} \] ✓ Mathematica : cpu = 0.378156 (sec), leaf count = 143
\[\text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {\left (\frac {8 K[1]}{K[2]}-\frac {2 \left (4 K[1] K[2]^2+1\right )}{K[2]^3}\right ) F'\left (\frac {4 K[1] K[2]^2+1}{K[2]^2}\right )}{F\left (\frac {4 K[1] K[2]^2+1}{K[2]^2}\right )^2}dK[1]+\frac {1}{K[2]^2}+\frac {1}{2 F\left (\frac {4 x K[2]^2+1}{K[2]^2}\right ) K[2]^3}\right )dK[2]+\int _1^x-\frac {1}{F\left (\frac {4 K[1] y(x)^2+1}{y(x)^2}\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.176 (sec), leaf count = 30
\[ \left \{ -{\it \_C1}- \left ( y \left ( x \right ) \right ) ^{-1}-{\frac {\int ^{4\,x+ \left ( y \left ( x \right ) \right ) ^{-2}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{4}}=0 \right \} \]