\[ y'(x)=\frac {y(x)^2 \left (x^2 F\left (\frac {x^2-y(x)}{x^2 y(x)}\right )+2\right )}{x^3} \] ✓ Mathematica : cpu = 0.509008 (sec), leaf count = 167
\[\text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x-\frac {2 \left (-\frac {K[1]^2-K[2]}{K[1]^2 K[2]^2}-\frac {1}{K[1]^2 K[2]}\right ) F'\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )}{F\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )^2 K[1]^3}dK[1]-\frac {1}{F\left (\frac {x^2-K[2]}{x^2 K[2]}\right ) K[2]^2}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]}+\frac {2}{K[1]^3 F\left (\frac {K[1]^2-y(x)}{K[1]^2 y(x)}\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.127 (sec), leaf count = 33
\[y \relax (x ) = \frac {x^{2}}{\RootOf \left (-\ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1}\right ) x^{2}+1}\]