\[ y'(x)=\frac {x F(-(x-y(x)) (y(x)+x))}{y(x)} \] ✓ Mathematica : cpu = 41.7872 (sec), leaf count = 116
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {K[2]}{F\left (K[2]^2-x^2\right )-1}-\int _1^x \frac {2 K[1] K[2] F'\left (K[2]^2-K[1]^2\right )}{\left (F\left (K[2]^2-K[1]^2\right )-1\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x \frac {K[1] F\left (y(x)^2-K[1]^2\right )}{1-F\left (y(x)^2-K[1]^2\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.152 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it RootOf} \left ( -{x}^{2}+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {{x}^{2}+{\it RootOf} \left ( -{x}^{2}+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) } \right \} \]