\[ y'(x)=\frac {F(-(x-y(x)) (y(x)+x))+x}{y(x)} \] ✓ Mathematica : cpu = 0.193391 (sec), leaf count = 113
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F(-(x-K[2]) (x+K[2]))}-\int _1^x-\frac {2 K[1] K[2] F'(-(K[1]-K[2]) (K[1]+K[2]))}{F(-(K[1]-K[2]) (K[1]+K[2]))^2}dK[1]\right )dK[2]+\int _1^x\left (\frac {K[1]}{F(-(K[1]-y(x)) (K[1]+y(x)))}+1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.247 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it RootOf} \left ( -2\,x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {{x}^{2}+{\it RootOf} \left ( -2\,x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) } \right \} \]