\[ y'(x)=\frac {x}{F\left (x^2+y(x)^2\right )-y(x)} \] ✓ Mathematica : cpu = 0.286124 (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 = 0.132 (sec), leaf count = 28
\[\left \{-c_{1}+\frac {\left (\int _{}^{x^{2}+y \left (x \right )^{2}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}{2}-y \left (x \right ) = 0\right \}\]