\[ y'(x)=\frac {y(x) (y(x)+x)}{x \left (y(x)^3+x\right )} \] ✓ Mathematica : cpu = 0.269172 (sec), leaf count = 285
DSolve[Derivative[1][y][x] == (y[x]*(x + y[x]))/(x*(x + y[x]^3)),y[x],x]
\[\left \{\left \{y(x)\to \frac {2 \sqrt [3]{2} (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}+\frac {\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1+i \sqrt {3}\right ) (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1-i \sqrt {3}\right ) (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{6 \sqrt [3]{2}}\right \}\right \}\] ✓ Maple : cpu = 0.123 (sec), leaf count = 404
dsolve(diff(y(x),x) = y(x)*(y(x)+x)/x/(x+y(x)^3),y(x))
\[y \left (x \right ) = \frac {\left (27 x +3 \sqrt {-24 c_{1}^{3}-72 c_{1}^{2} \ln \left (x \right )-72 c_{1} \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+6 \ln \left (x \right )+6 c_{1}}{3 \left (27 x +3 \sqrt {-24 c_{1}^{3}-72 c_{1}^{2} \ln \left (x \right )-72 c_{1} \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{\frac {1}{3}}}\]