\[ y'(x)=\frac {x^2+2 x y(x)+e^{-2 (x-y(x)) (y(x)+x)}+y(x)^2}{x^2+2 x y(x)-e^{-2 (x-y(x)) (y(x)+x)}+y(x)^2} \] ✓ Mathematica : cpu = 1.35597 (sec), leaf count = 432
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {2 e^{2 (x-K[2]) (x+K[2])} K[2]}{-e^{2 (x-K[2]) (x+K[2])} x^2+e^{2 (x-K[2]) (x+K[2])} K[2]^2+1}-\int _1^x\left (-\frac {2 e^{2 (K[1]-K[2]) (K[1]+K[2])} K[1] (2 (K[1]-K[2])-2 (K[1]+K[2]))}{e^{2 (K[1]-K[2]) (K[1]+K[2])} K[1]^2-e^{2 (K[1]-K[2]) (K[1]+K[2])} K[2]^2-1}+\frac {2 e^{2 (K[1]-K[2]) (K[1]+K[2])} K[1] \left (e^{2 (K[1]-K[2]) (K[1]+K[2])} (2 (K[1]-K[2])-2 (K[1]+K[2])) K[1]^2-2 e^{2 (K[1]-K[2]) (K[1]+K[2])} K[2]-e^{2 (K[1]-K[2]) (K[1]+K[2])} K[2]^2 (2 (K[1]-K[2])-2 (K[1]+K[2]))\right )}{\left (e^{2 (K[1]-K[2]) (K[1]+K[2])} K[1]^2-e^{2 (K[1]-K[2]) (K[1]+K[2])} K[2]^2-1\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 e^{2 (K[1]-y(x)) (K[1]+y(x))} K[1]}{e^{2 (K[1]-y(x)) (K[1]+y(x))} K[1]^2-e^{2 (K[1]-y(x)) (K[1]+y(x))} y(x)^2-1}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.402 (sec), leaf count = 36
\[y \relax (x ) = {\mathrm e}^{\RootOf \left (-\textit {\_Z} +\int _{}^{{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x}\frac {1}{{\mathrm e}^{2 \textit {\_a}}+\textit {\_a}}d \textit {\_a} +c_{1}\right )}-x\]