\[ y'(x)=\frac {x^2+2 x y(x)+e^{2 (x-y(x))^2 (y(x)+x)^2}+y(x)^2}{x^2+2 x y(x)-e^{2 (x-y(x))^2 (y(x)+x)^2}+y(x)^2} \] ✓ Mathematica : cpu = 2.0394 (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 = 0.18 (sec), leaf count = 38
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -{\it \_Z}+\int ^{ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,{{\rm e}^{{\it \_Z}}}x}\! \left ( {{\rm e}^{2\,{{\it \_a}}^{2}}}+{\it \_a} \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }}-x \right \} \]