\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( xy \left ( x \right ) +1 \right ) \left ( {x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}y \left ( x \right ) +2\,xy \left ( x \right ) +1+x+{x}^{2} \right ) }{{x}^{5}}}=0} \]
Mathematica: cpu = 0.157520 (sec), leaf count = 103 \[ \text {Solve}\left [-\frac {17}{3} \text {RootSum}\left [-17 \text {$\#$1}^3+3 \sqrt [3]{-34} \text {$\#$1}-17\& ,\frac {\log \left (\frac {\frac {x+3}{x^3}+\frac {3 y(x)}{x^2}}{\sqrt [3]{34} \sqrt [3]{-\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{-34}-17 \text {$\#$1}^2}\& \right ]=c_1-\frac {1}{9} 34^{2/3} \left (-\frac {1}{x^6}\right )^{2/3} x^3,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\frac {17\,{\it RootOf} \left ( 162\, \int ^{{\it \_Z}}\! \left ( 289\,{{\it \_a}}^{3}+54\,{\it \_a}-54 \right ) ^{-1}{d{\it \_a}}x+3\,x{\it \_C1}+2 \right ) x-3\,x-9}{9\,x}} \right \} \]