\[ y'(x)=\frac {y(x) \left (x^3+x^2 y(x)+y(x)^2\right )}{(x-1) x^2 (y(x)+x)} \] ✓ Mathematica : cpu = 0.243062 (sec), leaf count = 68
DSolve[Derivative[1][y][x] == (y[x]*(x^3 + x^2*y[x] + y[x]^2))/((-1 + x)*x^2*(x + y[x])),y[x],x]
\[\text {Solve}\left [-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\log \left (\frac {y(x)}{x}\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}=\log (1-x)-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.314 (sec), leaf count = 61
dsolve(diff(y(x),x) = y(x)/x^2/(x-1)*(x^3+x^2*y(x)+y(x)^2)/(y(x)+x),y(x))
\[-\frac {\ln \left (\frac {y \left (x \right )^{2}+x y \left (x \right )+x^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {3}\, \arctan \left (\frac {\left (x +2 y \left (x \right )\right ) \sqrt {3}}{3 x}\right )}{3}+\ln \left (\frac {y \left (x \right )}{x}\right )-\ln \left (x -1\right )+\ln \left (x \right )-c_{1} = 0\]