\[ y'(x)=\frac {x}{F\left (x^2+y(x)^2\right )-y(x)} \] ✓ Mathematica : cpu = 41.4378 (sec), leaf count = 91
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {2 K[1] K[2] F'\left (K[1]^2+K[2]^2\right )}{F\left (K[1]^2+K[2]^2\right )^2} \, dK[1]-\frac {K[2]}{F\left (K[2]^2+x^2\right )}+1\right ) \, dK[2]+\int _1^x -\frac {K[1]}{F\left (K[1]^2+y(x)^2\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.155 (sec), leaf count = 28
\[ \left \{ -y \left ( x \right ) +{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{2}}-{\it \_C1}=0 \right \} \]