\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( -\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) x+\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) -x+{x}^{2}y \left ( x \right ) -{x}^{2}+{x}^{3}y \left ( x \right ) \right ) }{ \left ( x-1 \right ) x\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) }}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {can not solve} \]
Maple: cpu = 0.312 (sec), leaf count = 114 \[ \left \{ y \left ( x \right ) ={1{{\rm e}^{\int \!-{\frac {\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) x+{x}^{2}-\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) +x}{x \left ( x-1 \right ) \cosh \left ( \left ( 1 +x \right ) ^{-1} \right ) }}\,{\rm d}x}} \left ( \int \!-{\frac {x \left ( 1+x \right ) }{ \left ( x-1 \right ) \cosh \left ( \left ( 1+x \right ) ^{-1} \right ) }{{\rm e}^{\int \!-{\frac {\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) x+{x}^{2}-\cosh \left ( \left ( 1+x \right ) ^{-1} \right ) +x}{x \left ( x-1 \right ) \cosh \left ( \left ( 1 +x \right ) ^{-1} \right ) }}\,{\rm d}x}}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]