\[ y(x) \left (y(x)^3-2 x^3\right ) y'(x)+x \left (2 y(x)^3-x^3\right )=0 \] ✓ Mathematica : cpu = 0.0517894 (sec), leaf count = 139
\[\text {Solve}\left [\frac {1}{7} \text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3+3 \text {$\#$1}^2+\text {$\#$1}+1\& ,\frac {8 \text {$\#$1}^3 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+9 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+12 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{4 \text {$\#$1}^3+3 \text {$\#$1}^2+6 \text {$\#$1}+1}\& \right ]-\frac {1}{7} \log \left (1-\frac {y(x)}{x}\right )=c_1-\log (x),y(x)\right ]\]
✓ Maple : cpu = 0.516 (sec), leaf count = 1192
\[ \left \{ y \left ( x \right ) =-{\frac {\sqrt {3}x}{6} \left ( \sqrt {3}-3\,{\it RootOf} \left ( 3\,{\it \_Z}-\sqrt {3}-4\,{\it \_C1}+3\,{{\it \_Z}}^{3}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{{\it \_Z}}^{3}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{\it \_Z}-\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,\sqrt {3}{{\it \_Z}}^{2}+3\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{{\it \_Z}}^{4}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_C1}\,\sqrt {3}{{\it \_Z}}^{2}+7\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{{\it \_Z}}^{2}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}{\it \_Z}-3\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) \tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_Z}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}{{\it \_Z}}^{3}+3\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_C1}\,{\it \_Z}+4\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) \tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_C1}+3\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_C1}\,{{\it \_Z}}^{3}-\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {\it \_C1}\,\sqrt {3}+\sqrt {3}{\it \_C1}\,{{\it \_Z}}^{3}+3\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{{\it \_Z}}^{3}+\sqrt {3}{\it \_C1}\,{\it \_Z}+3\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,{\it \_Z}-\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_C1}\,\sqrt {3}-3\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) \tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {{\it \_Z}}^{3}+\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) \tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}-\sqrt {3}\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {{\it \_Z}}^{3}-\sqrt {3}\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {\it \_Z}+4\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) +3\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {{\it \_Z}}^{4}+7\,\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) {{\it \_Z}}^{2}-\sqrt {3}{{\it \_Z}}^{2}-7\,{{\it \_Z}}^{2}{\it \_C1}+\tan \left ( 7/6\,\sqrt {3}\ln \left ( 2 \right ) \right ) \tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) \sqrt {3}{{\it \_Z}}^{2}+4\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) +3\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {{\it \_Z}}^{4}+7\,\tan \left ( 1/6\,\sqrt {3}\ln \left ( {\frac {\sqrt {3}{\it \_Z}-3}{{x}^{7} \left ( 6\,\sqrt {3}{{\it \_Z}}^{3}-9\,{{\it \_Z}}^{4}+14\,\sqrt {3}{\it \_Z}-36\,{{\it \_Z}}^{2}-19 \right ) ^{2}}} \right ) \right ) {{\it \_Z}}^{2}-3\,{\it \_C1}\,{{\it \_Z}}^{4} \right ) \right ) } \right \} \]