\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}{x}^{7}+y \left ( x \right ) {x}^{4}+x-3 \right ) }{x}}=0} \]
Mathematica: cpu = 0.076010 (sec), leaf count = 101 \[ \text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\& ,\frac {\log \left (\frac {3 x^6 y(x)+x^3}{\sqrt [3]{7} \sqrt [3]{-x^9}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\& \right ]=c_1+\frac {7^{2/3} \left (-x^9\right )^{2/3}}{9 x^5},y(x)\right ] \]
Maple: cpu = 0.172 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{x}^{3}} \left ( \sqrt {3} \tan \left ( {\it RootOf} \left ( -\sqrt {3}\ln \left ( {\frac {9\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+9}{7\, \left ( -3\, \tan \left ( {\it \_Z} \right ) +\sqrt {3} \right ) ^{2}}} \right ) +3\, \sqrt {3}{\it \_C1}-2\,\sqrt {3}x-2\,{\it \_Z} \right ) \right ) -1 \right ) } \right \} \]