\[ y'(x)=\frac {-\exp \left (\frac {2 (x-y(x))^3 (y(x)+x)^3}{x^2-y(x)^2-1}\right )-x^2-2 x y(x)-y(x)^2}{\exp \left (\frac {2 (x-y(x))^3 (y(x)+x)^3}{x^2-y(x)^2-1}\right )-x^2-2 x y(x)-y(x)^2} \] ✓ Mathematica : cpu = 4.04824 (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 = 0.663 (sec), leaf count = 43
\[y \relax (x ) = {\mathrm e}^{\RootOf \left (-\textit {\_Z} +\int _{}^{{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x}\frac {1}{{\mathrm e}^{\frac {2 \textit {\_a}^{3}}{\textit {\_a} +1}}+\textit {\_a}}d \textit {\_a} +c_{1}\right )}-x\]