\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) }{x} \left ( -1-\cosh \left ( {\frac {1+x}{x-1}} \right ) x+\cosh \left ( {\frac {1+x}{x-1}} \right ) {x}^{2}y \left ( x \right ) -\cosh \left ( {\frac {1+x}{x-1}} \right ) {x}^{2}+\cosh \left ( {\frac {1+x}{x-1}} \right ) {x}^{3}y \left ( x \right ) \right ) }=0} \]
Mathematica: cpu = 2.027757 (sec), leaf count = 349 \[ \left \{\left \{y(x)\to \frac {\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}-\frac {1}{4} e x^2 \sinh \left (\frac {2}{x-1}\right )+\frac {x^2 \sinh \left (\frac {2}{x-1}\right )}{4 e}-\frac {1}{4} e x^2 \cosh \left (\frac {2}{x-1}\right )-\frac {x^2 \cosh \left (\frac {2}{x-1}\right )}{4 e}-e x \sinh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \sinh \left (\frac {2}{x-1}\right )-\frac {\sinh \left (\frac {2}{x-1}\right )}{4 e}-e x \cosh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \cosh \left (\frac {2}{x-1}\right )+\frac {\cosh \left (\frac {2}{x-1}\right )}{4 e}+\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )}{x \left (c_1 \exp \left (\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )+\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}\right )\right )}\right \}\right \} \]
Maple: cpu = 0.141 (sec), leaf count = 281 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{-{\frac {{\rm e}{x }^{2}}{4}{{\rm e}^{2\, \left ( x-1 \right ) ^{-1}}}}}}{{\rm e}^{{\frac { 5\,{\rm e}}{4}{{\rm e}^{2\, \left ( x-1 \right ) ^{-1}}}}}}{{\rm e}^{-{ \frac {{{\rm e}^{-1}}{x}^{2}}{4}{{\rm e}^{-2\, \left ( x-1 \right ) ^{-1 }}}}}}{{\rm e}^{{\frac {{{\rm e}^{-1}}}{4}{{\rm e}^{-2\, \left ( x-1 \right ) ^{-1}}}}}}{{\rm e}^{{{\rm e}^{-1}}{\it Ei} \left ( 1,2\, \left ( x-1 \right ) ^{-1} \right ) }} \left ( {{\rm e}^{{\rm e}{{\rm e}^ {2\, \left ( x-1 \right ) ^{-1}}}x}} \right ) ^{-1} \left ( {{\rm e}^{{ \rm e}{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) }} \right ) ^{-3} \left ( \int \!-{1{{\rm e}^{-{\frac {{\rm e}{x}^{2}}{4}{ {\rm e}^{2\, \left ( x-1 \right ) ^{-1}}}}}}{{\rm e}^{{\frac {5\,{\rm e} }{4}{{\rm e}^{2\, \left ( x-1 \right ) ^{-1}}}}}}{{\rm e}^{-{\frac {{ {\rm e}^{-1}}{x}^{2}}{4}{{\rm e}^{-2\, \left ( x-1 \right ) ^{-1}}}}}}{ {\rm e}^{{\frac {{{\rm e}^{-1}}}{4}{{\rm e}^{-2\, \left ( x-1 \right ) ^ {-1}}}}}}{{\rm e}^{{{\rm e}^{-1}}{\it Ei} \left ( 1,2\, \left ( x-1 \right ) ^{-1} \right ) }} \left ( x\cosh \left ( \left ( x-1 \right ) ^{- 1} \right ) \cosh \left ( {\frac {x}{x-1}} \right ) +x\sinh \left ( \left ( x-1 \right ) ^{-1} \right ) \sinh \left ( {\frac {x}{x-1}} \right ) +\cosh \left ( \left ( x-1 \right ) ^{-1} \right ) \cosh \left ( {\frac {x}{x-1}} \right ) +\sinh \left ( \left ( x-1 \right ) ^{-1} \right ) \sinh \left ( {\frac {x}{x-1}} \right ) \right ) \left ( { {\rm e}^{{\rm e}{{\rm e}^{2\, \left ( x-1 \right ) ^{-1}}}x}} \right ) ^{ -1} \left ( {{\rm e}^{{\rm e}{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) }} \right ) ^{-3}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]