\[ y'(x)=\frac {\text {sech}\left (\frac {1}{x-1}\right ) \left (x^5+x^4-2 x^3 y(x)-2 x^2 y(x)+2 x^2 \cosh \left (\frac {1}{x-1}\right )+x y(x)^2+y(x)^2-x-2 x \cosh \left (\frac {1}{x-1}\right )-1\right )}{x-1} \] ✓ Mathematica : cpu = 6.99969 (sec), leaf count = 110
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {2 (K[5]+1) \text {sech}\left (\frac {1}{K[5]-1}\right )}{K[5]-1}dK[5]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[6]}\frac {2 (K[5]+1) \text {sech}\left (\frac {1}{K[5]-1}\right )}{K[5]-1}dK[5]\right ) (K[6]+1) \text {sech}\left (\frac {1}{K[6]-1}\right )}{K[6]-1}dK[6]+c_1}+\frac {x^3+x^2}{x+1}+1\right \}\right \}\] ✓ Maple : cpu = 7.334 (sec), leaf count = 306
\[y \relax (x ) = \frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {\int \frac {4 \,{\mathrm e}^{\frac {1}{x -1}} \left (1+x \right )}{\left ({\mathrm e}^{\frac {2}{x -1}}+1\right ) \left (x -1\right )}d x}{{\mathrm e}^{\frac {2}{x -1}}+1}} {\mathrm e}^{\frac {\left (\int \frac {4 \,{\mathrm e}^{\frac {1}{x -1}} \left (1+x \right )}{\left ({\mathrm e}^{\frac {2}{x -1}}+1\right ) \left (x -1\right )}d x \right ) {\mathrm e}^{\frac {2}{x -1}}}{{\mathrm e}^{\frac {2}{x -1}}+1}}+{\mathrm e}^{\frac {4 c_{1} {\mathrm e}^{\frac {2}{x -1}}}{{\mathrm e}^{\frac {2}{x -1}}+1}} {\mathrm e}^{\frac {4 c_{1}}{{\mathrm e}^{\frac {2}{x -1}}+1}} \left (x^{2}+1\right )}{{\mathrm e}^{\frac {4 c_{1} {\mathrm e}^{\frac {2}{x -1}}}{{\mathrm e}^{\frac {2}{x -1}}+1}} {\mathrm e}^{\frac {4 c_{1}}{{\mathrm e}^{\frac {2}{x -1}}+1}}-{\mathrm e}^{\frac {\left (\int \frac {4 \,{\mathrm e}^{\frac {1}{x -1}} \left (1+x \right )}{\left ({\mathrm e}^{\frac {2}{x -1}}+1\right ) \left (x -1\right )}d x \right ) {\mathrm e}^{\frac {2}{x -1}}}{{\mathrm e}^{\frac {2}{x -1}}+1}} {\mathrm e}^{\frac {\int \frac {4 \,{\mathrm e}^{\frac {1}{x -1}} \left (1+x \right )}{\left ({\mathrm e}^{\frac {2}{x -1}}+1\right ) \left (x -1\right )}d x}{{\mathrm e}^{\frac {2}{x -1}}+1}}}\]