\[ y'(x)=\frac {y(x) \left (x^3 y(x) \cosh \left (\frac {x+1}{x-1}\right )+x^2 y(x) \cosh \left (\frac {x+1}{x-1}\right )-x^2 \cosh \left (\frac {x+1}{x-1}\right )-x \cosh \left (\frac {x+1}{x-1}\right )-1\right )}{x} \] ✓ Mathematica : cpu = 2.13721 (sec), leaf count = 349
\[\left \{\left \{y(x)\to \frac {\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}-\frac {1}{4} e x^2 \sinh \left (\frac {2}{x-1}\right )+\frac {x^2 \sinh \left (\frac {2}{x-1}\right )}{4 e}-\frac {1}{4} e x^2 \cosh \left (\frac {2}{x-1}\right )-\frac {x^2 \cosh \left (\frac {2}{x-1}\right )}{4 e}-e x \sinh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \sinh \left (\frac {2}{x-1}\right )-\frac {\sinh \left (\frac {2}{x-1}\right )}{4 e}-e x \cosh \left (\frac {2}{x-1}\right )+\frac {5}{4} e \cosh \left (\frac {2}{x-1}\right )+\frac {\cosh \left (\frac {2}{x-1}\right )}{4 e}+\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )}{x \left (\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}\right )+c_1 \exp \left (\frac {(x-1) \left (\left (-x+e^2 (x+5)-1\right ) \sinh \left (\frac {2}{x-1}\right )+\left (x+e^2 (x+5)+1\right ) \cosh \left (\frac {2}{x-1}\right )\right )}{4 e}\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.696 (sec), leaf count = 168
\[\left \{y \left (x \right ) = \frac {{\mathrm e}^{-3 \,{\mathrm e} \Ei \left (1, -\frac {2}{x -1}\right )+{\mathrm e}^{-1} \Ei \left (1, \frac {2}{x -1}\right )-\frac {\left (x^{2}-1\right ) {\mathrm e}^{\frac {-x -1}{x -1}}}{4}-\frac {\left (x^{2}+4 x -5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}}}{\left (c_{1}+\int -\left (x +1\right ) \cosh \left (\frac {x +1}{x -1}\right ) {\mathrm e}^{-3 \,{\mathrm e} \Ei \left (1, -\frac {2}{x -1}\right )+{\mathrm e}^{-1} \Ei \left (1, \frac {2}{x -1}\right )+\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-x -1}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{4}}d x \right ) x}\right \}\]