\[ y'(x)=\frac {x}{F\left (x^2+y(x)^2\right )-y(x)} \] ✓ Mathematica : cpu = 0.228246 (sec), leaf count = 94
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F\left (x^2+K[2]^2\right )}-\int _1^x\frac {2 K[1] K[2] F'\left (K[1]^2+K[2]^2\right )}{F\left (K[1]^2+K[2]^2\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{F\left (K[1]^2+y(x)^2\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.207 (sec), leaf count = 28
\[ \left \{ -y \left ( x \right ) +{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}}{2}}-{\it \_C1}=0 \right \} \]