\[ y'(x)=\frac {x^4 \coth \left (\frac {x+1}{x-1}\right )-2 x^2 y(x) \coth \left (\frac {x+1}{x-1}\right )+y(x)^2 \coth \left (\frac {x+1}{x-1}\right )+2 x \log \left (\frac {1}{x-1}\right )-\coth \left (\frac {x+1}{x-1}\right )}{\log \left (\frac {1}{x-1}\right )} \] ✓ Mathematica : cpu = 71.9734 (sec), leaf count = 127
DSolve[Derivative[1][y][x] == (-Coth[(1 + x)/(-1 + x)] + x^4*Coth[(1 + x)/(-1 + x)] + 2*x*Log[(-1 + x)^(-1)] - 2*x^2*Coth[(1 + x)/(-1 + x)]*y[x] + Coth[(1 + x)/(-1 + x)]*y[x]^2)/Log[(-1 + x)^(-1)],y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {2 \coth \left (\frac {K[5]}{K[5]-1}+\frac {1}{K[5]-1}\right )}{\log \left (\frac {1}{K[5]-1}\right )}dK[5]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[6]}\frac {2 \coth \left (\frac {K[5]}{K[5]-1}+\frac {1}{K[5]-1}\right )}{\log \left (\frac {1}{K[5]-1}\right )}dK[5]\right ) \coth \left (\frac {K[6]}{K[6]-1}+\frac {1}{K[6]-1}\right )}{\log \left (\frac {1}{K[6]-1}\right )}dK[6]+c_1}+x^2+1\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(y(x),x) = (2*x*ln(1/(x-1))-coth((1+x)/(x-1))+coth((1+x)/(x-1))*y(x)^2-2*coth((1+x)/(x-1))*x^2*y(x)+coth((1+x)/(x-1))*x^4)/ln(1/(x-1)),y(x))
, could not solve
dsolve(diff(y(x),x) = (2*x*ln(1/(x-1))-coth((1+x)/(x-1))+coth((1+x)/(x-1))*y(x)^2-2*coth((1+x)/(x-1))*x^2*y(x)+coth((1+x)/(x-1))*x^4)/ln(1/(x-1)),y(x))