\[ y'(x)=\frac {y(x) \text {sech}\left (\frac {1}{x+1}\right ) \left (x^3 y(x)+x^2 y(x)-x^2-x-x \cosh \left (\frac {1}{x+1}\right )+\cosh \left (\frac {1}{x+1}\right )\right )}{(x-1) x} \] ✓ Mathematica : cpu = 2.7716 (sec), leaf count = 157
DSolve[Derivative[1][y][x] == (Sech[(1 + x)^(-1)]*y[x]*(-x - x^2 + Cosh[(1 + x)^(-1)] - x*Cosh[(1 + x)^(-1)] + x^2*y[x] + x^3*y[x]))/((-1 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]^2-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]-K[1]+1}{(K[1]-1) K[1]}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]^2-\text {sech}\left (\frac {1}{K[1]+1}\right ) K[1]-K[1]+1}{(K[1]-1) K[1]}dK[1]\right ) \left (\text {sech}\left (\frac {1}{K[2]+1}\right ) K[2]^3+\text {sech}\left (\frac {1}{K[2]+1}\right ) K[2]^2\right )}{(K[2]-1) K[2]}dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.302 (sec), leaf count = 112
dsolve(diff(y(x),x) = y(x)*(-cosh(1/(1+x))*x+cosh(1/(1+x))-x+x^2*y(x)-x^2+x^3*y(x))/x/(x-1)/cosh(1/(1+x)),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {\left (1-x \right ) \cosh \left (\frac {1}{1+x}\right )-x^{2}-x}{x \left (x -1\right ) \cosh \left (\frac {1}{1+x}\right )}d x}}{\int -\frac {{\mathrm e}^{\int \frac {\left (1-x \right ) \cosh \left (\frac {1}{1+x}\right )-x^{2}-x}{x \left (x -1\right ) \cosh \left (\frac {1}{1+x}\right )}d x} x \left (1+x \right )}{\cosh \left (\frac {1}{1+x}\right ) \left (x -1\right )}d x +c_{1}}\]