\[ y'(x)=\frac {F(-(x-y(x)) (y(x)+x))+x}{y(x)} \] ✓ Mathematica : cpu = 38.2493 (sec), leaf count = 99
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {2 K[1] K[2] F'\left (K[2]^2-K[1]^2\right )}{F\left (K[2]^2-K[1]^2\right )^2} \, dK[1]-\frac {K[2]}{F\left (K[2]^2-x^2\right )}\right ) \, dK[2]+\int _1^x \left (\frac {K[1]}{F\left (y(x)^2-K[1]^2\right )}+1\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.773 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it RootOf} \left ( -2\,x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {{x}^{2}+{\it RootOf} \left ( -2\,x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) } \right \} \]