\[ y'(x)=\frac {x}{F\left (x^2+y(x)^2\right )-y(x)} \] ✓ Mathematica : cpu = 0.2465 (sec), leaf count = 94
DSolve[Derivative[1][y][x] == x/(F[x^2 + y[x]^2] - y[x]),y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F\left (x^2+K[2]^2\right )}-\int _1^x\frac {2 K[1] K[2] F'\left (K[1]^2+K[2]^2\right )}{F\left (K[1]^2+K[2]^2\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{F\left (K[1]^2+y(x)^2\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.144 (sec), leaf count = 28
dsolve(diff(y(x),x) = x/(-y(x)+F(y(x)^2+x^2)),y(x))
\[-y \left (x \right )+\frac {\left (\int _{}^{y \left (x \right )^{2}+x^{2}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}{2}-c_{1} = 0\]