\[ y'(x)=\frac {y(x) \text {sech}\left (\frac {1}{x+1}\right ) \left (x^3 y(x)+x^2 y(x)-x^2-x-x \cosh \left (\frac {1}{x+1}\right )+\cosh \left (\frac {1}{x+1}\right )\right )}{(x-1) x} \] ✓ Mathematica : cpu = 2.72693 (sec), leaf count = 157
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]^2-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]-K[1]+1}{(K[1]-1) K[1]}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]^2-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]-K[1]+1}{(K[1]-1) K[1]}dK[1]\right ) \left (\text {sech}\left (\frac {1}{K[2]+1}\right ) K[2]^3+\text {sech}\left (\frac {1}{K[2]+1}\right ) K[2]^2\right )}{(K[2]-1) K[2]}dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.726 (sec), leaf count = 112
\[ \left \{ y \left ( x \right ) ={{{\rm e}^{\int \!{\frac { \left ( 1-x \right ) \cosh \left ( \left ( 1+x \right ) ^{-1} \right ) -{x}^{2}-x}{x \left ( x-1 \right ) \cosh \left ( \left ( 1+x \right ) ^{-1} \right ) }}\,{\rm d}x}} \left ( \int \!-{\frac {x \left ( 1+x \right ) }{\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) \left ( x-1 \right ) }{{\rm e}^{\int \!{\frac { \left ( 1-x \right ) \cosh \left ( \left ( 1+x \right ) ^{-1} \right ) -{x}^{2}-x}{x \left ( x-1 \right ) \cosh \left ( \left ( 1+x \right ) ^{-1} \right ) }}\,{\rm d}x}}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]