\[ y'(x)=\frac {\exp \left (-2 x^6+6 x^4 y(x)^2+2 x^4-6 x^2 y(x)^4-4 x^2 y(x)^2+2 y(x)^6+2 y(x)^4+2\right )+x^2+2 x y(x)+y(x)^2}{-\exp \left (-2 x^6+6 x^4 y(x)^2+2 x^4-6 x^2 y(x)^4-4 x^2 y(x)^2+2 y(x)^6+2 y(x)^4+2\right )+x^2+2 x y(x)+y(x)^2} \] ✓ Mathematica : cpu = 4.73342 (sec), leaf count = 813
DSolve[Derivative[1][y][x] == (E^(2 + 2*x^4 - 2*x^6 - 4*x^2*y[x]^2 + 6*x^4*y[x]^2 + 2*y[x]^4 - 6*x^2*y[x]^4 + 2*y[x]^6) + x^2 + 2*x*y[x] + y[x]^2)/(-E^(2 + 2*x^4 - 2*x^6 - 4*x^2*y[x]^2 + 6*x^4*y[x]^2 + 2*y[x]^4 - 6*x^2*y[x]^4 + 2*y[x]^6) + x^2 + 2*x*y[x] + y[x]^2),y[x],x]
\[\text {Solve}\left [\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} K[1]}{e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} K[1]^2-e^{2 y(x)^6+2 y(x)^4+6 K[1]^4 y(x)^2+2 K[1]^4+2}-e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} y(x)^2}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} K[2]}{-e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} x^2+e^{2 K[2]^6+2 K[2]^4+6 x^4 K[2]^2+2 x^4+2}+e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} K[2]^2}-\int _1^x\left (-\frac {2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1] \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right )}{e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1]^2-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2}-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2}+\frac {2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1] \left (e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right ) K[1]^2-2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2 \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right )-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2} \left (12 K[2]^5+8 K[2]^3+12 K[1]^4 K[2]\right )\right )}{\left (e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1]^2-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2}-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.4 (sec), leaf count = 45
dsolve(diff(y(x),x) = (y(x)^2+2*x*y(x)+x^2+exp(2+2*y(x)^4-4*x^2*y(x)^2+2*x^4+2*y(x)^6-6*x^2*y(x)^4+6*x^4*y(x)^2-2*x^6))/(y(x)^2+2*x*y(x)+x^2-exp(2+2*y(x)^4-4*x^2*y(x)^2+2*x^4+2*y(x)^6-6*x^2*y(x)^4+6*x^4*y(x)^2-2*x^6)),y(x))
\[y \left (x \right ) = {\mathrm e}^{\RootOf \left (-\textit {\_Z} +\int _{}^{{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x}\frac {1}{{\mathrm e}^{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+2}+\textit {\_a}}d \textit {\_a} +c_{1}\right )}-x\]