\[ y'(x)=\frac {y(x) \left (x^3 y(x) \cosh \left (\frac {x+1}{x-1}\right )+x^2 y(x) \cosh \left (\frac {x+1}{x-1}\right )-x^2 \cosh \left (\frac {x+1}{x-1}\right )-x \cosh \left (\frac {x+1}{x-1}\right )-1\right )}{x} \] ✓ Mathematica : cpu = 1.24112 (sec), leaf count = 307
DSolve[Derivative[1][y][x] == (y[x]*(-1 - x*Cosh[(1 + x)/(-1 + x)] - x^2*Cosh[(1 + x)/(-1 + x)] + x^2*Cosh[(1 + x)/(-1 + x)]*y[x] + x^3*Cosh[(1 + x)/(-1 + x)]*y[x]))/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\frac {1}{4} e^{\frac {x}{x-1}+\frac {3}{x-1}} \left (4 \left (3-\frac {1}{e^2}\right ) e^{-\frac {4}{x-1}} \text {Chi}\left (\frac {2}{x-1}\right )+e^{-\frac {2 x}{x-1}-\frac {4}{x-1}} \left (4 \left (e^{\frac {2}{x-1}}+3 e^{\frac {2 x}{x-1}}\right ) \text {Shi}\left (\frac {2}{x-1}\right )-\left ((x-1) \left (x+e^{\frac {2 x}{x-1}+\frac {2}{x-1}} (x+5)+1\right )\right )-4 e^{\frac {x}{x-1}+\frac {1}{x-1}} \log (x)\right )\right )+\frac {1}{4} e^{-\frac {2}{x-1}-1} x^2+\frac {1}{4} e^{\frac {2 x}{x-1}-1} \left (x^2+4 x-5\right )\right )}{\exp \left (\frac {\left (3 e^2-1\right ) \text {Chi}\left (\frac {2}{x-1}\right )}{e}+\frac {\left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{x-1}\right )}{e}+\frac {1}{4} e^{-\frac {2}{x-1}-1}\right )+c_1 \exp \left (\frac {1}{4} e^{-\frac {2}{x-1}-1} x^2+\frac {1}{4} e^{\frac {2 x}{x-1}-1} \left (x^2+4 x-5\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 1.303 (sec), leaf count = 168
dsolve(diff(y(x),x) = y(x)*(-1-cosh((1+x)/(x-1))*x+cosh((1+x)/(x-1))*x^2*y(x)-cosh((1+x)/(x-1))*x^2+cosh((1+x)/(x-1))*x^3*y(x))/x,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{-\frac {\left (x^{2}-1\right ) {\mathrm e}^{\frac {-1-x}{x -1}}}{4}-\frac {\left (x^{2}+4 x -5\right ) {\mathrm e}^{\frac {1+x}{x -1}}}{4}+\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) {\mathrm e}^{-1}-3 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (c_{1}+\int -{\mathrm e}^{\frac {\left (-x^{2}+1\right ) {\mathrm e}^{\frac {-1-x}{x -1}}}{4}+\frac {\left (-x^{2}-4 x +5\right ) {\mathrm e}^{\frac {1+x}{x -1}}}{4}+\operatorname {expIntegral}_{1}\left (\frac {2}{x -1}\right ) {\mathrm e}^{-1}-3 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )} \left (1+x \right ) \cosh \left (\frac {1+x}{x -1}\right )d x \right )}\]