\[ y'(x)=\frac {y(x)^2+x y(x)+x}{(x-1) (y(x)+x)} \] ✓ Mathematica : cpu = 0.196742 (sec), leaf count = 61
DSolve[Derivative[1][y][x] == (x + x*y[x] + y[x]^2)/((-1 + x)*(x + y[x])),y[x],x]
\[\text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}=\log (1-x)-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.285 (sec), leaf count = 48
dsolve(diff(y(x),x) = 1/(x-1)*(x*y(x)+x+y(x)^2)/(y(x)+x),y(x))
\[y \left (x \right ) = -\frac {x}{2}+\frac {\sqrt {3}\, x \tan \left (\RootOf \left (-\sqrt {3}\, \ln \left (\frac {3 x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}{4 \left (x -1\right )^{2}}\right )+2 \sqrt {3}\, c_{1}-2 \textit {\_Z} \right )\right )}{2}\]