\[ y'(x)=-\frac {1}{8} x (y(x)+1)^2 (-\log (y(x)-1)+\log (y(x)+1)+2 \log (x)) \] ✓ Mathematica : cpu = 33.4825 (sec), leaf count = 610
DSolve[Derivative[1][y][x] == -1/8*(x*(2*Log[x] - Log[-1 + y[x]] + Log[1 + y[x]])*(1 + y[x])^2),y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {-2 \log (x) x^2+\log (K[2]-1) x^2-\log (K[2]+1) x^2-8}{2 \left (2 \log (x) x^2-\log (K[2]-1) x^2+\log (K[2]+1) x^2+K[2] \left (2 \log (x) x^2-\log (K[2]-1) x^2+\log (K[2]+1) x^2+8\right )-8\right )}-\int _1^x\left (-\frac {K[1] (K[2]+1) \left (\frac {1}{K[2]+1}-\frac {1}{K[2]-1}\right )}{2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8}-\frac {K[1] (2 \log (K[1])-\log (K[2]-1)+\log (K[2]+1))}{2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8}+\frac {K[1] (K[2]+1) (2 \log (K[1])-\log (K[2]-1)+\log (K[2]+1)) \left (-\frac {K[2] K[1]^2}{K[2]-1}+2 \log (K[1]) K[1]^2-\log (K[2]-1) K[1]^2+\log (K[2]+1) K[1]^2-\frac {K[1]^2}{K[2]-1}+\frac {K[2] K[1]^2}{K[2]+1}+\frac {K[1]^2}{K[2]+1}+8\right )}{\left (2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8\right )^2}\right )dK[1]+\frac {1}{2 (K[2]+1)}\right )dK[2]+\int _1^x-\frac {K[1] (2 \log (K[1])-\log (y(x)-1)+\log (y(x)+1)) (y(x)+1)}{2 \log (K[1]) K[1]^2-\log (y(x)-1) K[1]^2+\log (y(x)+1) K[1]^2+2 \log (K[1]) y(x) K[1]^2-\log (y(x)-1) y(x) K[1]^2+\log (y(x)+1) y(x) K[1]^2+8 y(x)-8}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.678 (sec), leaf count = 65
dsolve(diff(y(x),x) = -1/8*(-ln(-1+y(x))+ln(1+y(x))+2*ln(x))*x*(1+y(x))^2,y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{2 \left (-\frac {x^{2} \left (1+\textit {\_a} \right ) \ln \left (\textit {\_a} -1\right )}{2}+\frac {x^{2} \left (1+\textit {\_a} \right ) \ln \left (1+\textit {\_a} \right )}{2}+x^{2} \left (1+\textit {\_a} \right ) \ln \left (x \right )+4 \textit {\_a} -4\right ) \left (1+\textit {\_a} \right )}d \textit {\_a} +\frac {\ln \left (x \right )}{8}-c_{1} = 0\]