\[ y'(x)=\frac {-\exp \left (\frac {2 (x-y(x))^3 (y(x)+x)^3}{x^2-y(x)^2-1}\right )-x^2-2 x y(x)-y(x)^2}{\exp \left (\frac {2 (x-y(x))^3 (y(x)+x)^3}{x^2-y(x)^2-1}\right )-x^2-2 x y(x)-y(x)^2} \] ✓ Mathematica : cpu = 4.64022 (sec), leaf count = 349
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {2 K[2]}{-x^2+\exp \left (\frac {2 (x-K[2])^3 (x+K[2])^3}{x^2-K[2]^2-1}\right )+K[2]^2}-\int _1^x\left (\frac {2 K[1] \left (-2 K[2]-\exp \left (\frac {2 (K[1]-K[2])^3 (K[1]+K[2])^3}{K[1]^2-K[2]^2-1}\right ) \left (\frac {6 (K[1]+K[2])^2 (K[1]-K[2])^3}{K[1]^2-K[2]^2-1}+\frac {4 K[2] (K[1]+K[2])^3 (K[1]-K[2])^3}{\left (K[1]^2-K[2]^2-1\right )^2}-\frac {6 (K[1]+K[2])^3 (K[1]-K[2])^2}{K[1]^2-K[2]^2-1}\right )\right )}{\left (K[1]^2-\exp \left (\frac {2 (K[1]-K[2])^3 (K[1]+K[2])^3}{K[1]^2-K[2]^2-1}\right )-K[2]^2\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 K[1]}{K[1]^2-\exp \left (\frac {2 (K[1]-y(x))^3 (K[1]+y(x))^3}{K[1]^2-y(x)^2-1}\right )-y(x)^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.792 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -{\it \_Z}+\int ^{ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}}\! \left ( {{\rm e}^{2\,{\frac {{{\it \_a}}^{3}}{{\it \_a}+1}}}}+{\it \_a} \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }}-x \right \} \]