\[ y'(x)=\frac {y(x)^2 \left (x^2 F\left (\frac {x^2-y(x)}{x^2 y(x)}\right )+2\right )}{x^3} \] ✓ Mathematica : cpu = 224.98 (sec), leaf count = 164
\[\text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x -\frac {2 \left (-\frac {K[1]^2-K[2]}{K[1]^2 K[2]^2}-\frac {1}{K[1]^2 K[2]}\right ) F'\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )}{K[1]^3 F\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )^2} \, dK[1]-\frac {1}{K[2]^2 F\left (\frac {x^2-K[2]}{x^2 K[2]}\right )}\right ) \, dK[2]+\int _1^x \left (\frac {2}{K[1]^3 F\left (\frac {K[1]^2-y(x)}{y(x) K[1]^2}\right )}+\frac {1}{K[1]}\right ) \, dK[1]=c_1,y(x)\right ]\]
✓ Maple : cpu = 0.144 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{{\it RootOf} \left ( -\ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) {x}^{2}+1}} \right \} \]