\[ y'(x)=\frac {x^2+2 x y(x)+e^{2 (x-y(x))^2 (y(x)+x)^2}+y(x)^2}{x^2+2 x y(x)-e^{2 (x-y(x))^2 (y(x)+x)^2}+y(x)^2} \] ✓ Mathematica : cpu = 2.25506 (sec), leaf count = 228
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {2 K[2]}{-x^2+e^{2 (x-K[2])^2 (x+K[2])^2}+K[2]^2}-\int _1^x\left (\frac {2 K[1] \left (-2 K[2]-e^{2 (K[1]-K[2])^2 (K[1]+K[2])^2} \left (4 (K[1]-K[2])^2 (K[1]+K[2])-4 (K[1]-K[2]) (K[1]+K[2])^2\right )\right )}{\left (K[1]^2-e^{2 (K[1]-K[2])^2 (K[1]+K[2])^2}-K[2]^2\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 K[1]}{K[1]^2-e^{2 (K[1]-y(x))^2 (K[1]+y(x))^2}-y(x)^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.312 (sec), leaf count = 38
\[\left \{y \left (x \right ) = -x +{\mathrm e}^{\RootOf \left (c_{1}-\textit {\_Z} +\int _{}^{-2 x \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{2 \textit {\_Z}}}\frac {1}{\textit {\_a} +{\mathrm e}^{2 \textit {\_a}^{2}}}d \textit {\_a} \right )}\right \}\]