\[ y'(x)=\frac {1}{x y(x) \left (x y(x)^2+x+1\right )} \] ✓ Mathematica : cpu = 0.15342 (sec), leaf count = 76
\[\left \{\left \{y(x)\to -\frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-\frac {1}{2}}\right )+x-1}}{\sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-\frac {1}{2}}\right )+x-1}}{\sqrt {x}}\right \}\right \}\] ✓ Maple : cpu = 0.143 (sec), leaf count = 62
\[y \relax (x ) = \frac {\sqrt {x \left (2 \LambertW \left (\frac {c_{1} {\mathrm e}^{-\frac {x -1}{2 x}}}{2}\right ) x +x -1\right )}}{x}\]