\[ y'(x)=\frac {F\left (x^2+y(x)^2\right )-x}{y(x)} \] ✓ Mathematica : cpu = 0.191244 (sec), leaf count = 95
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F\left (x^2+K[2]^2\right )}-\int _1^x\frac {2 K[1] K[2] F'\left (K[1]^2+K[2]^2\right )}{F\left (K[1]^2+K[2]^2\right )^2}dK[1]\right )dK[2]+\int _1^x\left (1-\frac {K[1]}{F\left (K[1]^2+y(x)^2\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.095 (sec), leaf count = 57
\[\left \{y \left (x \right ) = \sqrt {-x^{2}+\RootOf \left (2 c_{1}-2 x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}, y \left (x \right ) = -\sqrt {-x^{2}+\RootOf \left (2 c_{1}-2 x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}\right \}\]