\[ 2 \left (x y'(x)+y(x)\right )^3-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 2.02633 (sec), leaf count = 179
DSolve[-(y[x]*Derivative[1][y][x]) + 2*(y[x] + x*Derivative[1][y][x])^3 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\int _1^x\frac {\text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3} \arctan \left (\sqrt {8 \text {$\#$1}-1}\right )}{\text {$\#$1} \sqrt {8 \text {$\#$1}-1}}-14 \log \left (\text {$\#$1}^2 (8 \text {$\#$1}-1)\right )+\log \left (\text {$\#$1}^{14} (8 \text {$\#$1}-1)^{15/2} \left (\text {$\#$1}-\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\log \left (\text {$\#$1}^{12} (8 \text {$\#$1}-1)^{13/2} \left (\text {$\#$1}+\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\frac {3 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}}{\text {$\#$1}}\& \right ][c_1+2 \log (K[1])]}{K[1]}dK[1]}{x}\right \}\right \}\] ✓ Maple : cpu = 3.818 (sec), leaf count = 1725
dsolve(2*(x*diff(y(x),x)+y(x))^3-y(x)*diff(y(x),x)=0,y(x))
\[\int _{\textit {\_b}}^{x}\frac {-6^{\frac {2}{3}} \left (-9 \textit {\_a}^{2} y \left (x \right ) \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} y \left (x \right )^{2}-2 y \left (x \right )}{\textit {\_a}}}}{9}+y \left (x \right )\right )\right )^{\frac {2}{3}}+6 \textit {\_a} y \left (x \right ) \left (6^{\frac {1}{3}} \left (-9 \textit {\_a}^{2} y \left (x \right ) \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} y \left (x \right )^{2}-2 y \left (x \right )}{\textit {\_a}}}}{9}+y \left (x \right )\right )\right )^{\frac {1}{3}}-1\right )}{6 \textit {\_a}^{2} y \left (x \right )+\textit {\_a} 6^{\frac {2}{3}} \left (-9 \textit {\_a}^{2} y \left (x \right ) \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} y \left (x \right )^{2}-2 y \left (x \right )}{\textit {\_a}}}}{9}+y \left (x \right )\right )\right )^{\frac {2}{3}}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (\frac {6 x 6^{\frac {1}{3}} \left (-9 \textit {\_f} \,x^{2} \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_f}^{2} x -2 \textit {\_f}}{x}}}{9}+\textit {\_f} \right )\right )^{\frac {1}{3}}}{6^{\frac {2}{3}} \left (-9 \textit {\_f} \,x^{2} \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_f}^{2} x -2 \textit {\_f}}{x}}}{9}+\textit {\_f} \right )\right )^{\frac {2}{3}}+6 x \textit {\_f}}-\left (\int _{\textit {\_b}}^{x}\frac {324 \textit {\_f} \textit {\_a} \left (\frac {\left (\frac {\textit {\_f} \sqrt {3}\, \left (\textit {\_a} \textit {\_f} -\frac {1}{27}\right )}{\sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}-\frac {2 \textit {\_a} \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}{18}+\textit {\_f} \right )}{3}\right ) \textit {\_f} \textit {\_a}}{\left (-9 \textit {\_f} \,\textit {\_a}^{2} \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}{9}+\textit {\_f} \right )\right )^{\frac {2}{3}}}-\frac {6^{\frac {2}{3}} \left (\frac {\textit {\_f} \sqrt {3}\, \left (\textit {\_a} \textit {\_f} -\frac {1}{27}\right )}{\sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}+\frac {\textit {\_a} \left (-\frac {2 \sqrt {3}\, \sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}{9}+\textit {\_f} \right )}{3}\right )}{6}\right ) 6^{\frac {1}{3}}}{\left (6^{\frac {2}{3}} \left (-9 \textit {\_f} \,\textit {\_a}^{2} \left (-\frac {\sqrt {3}\, \sqrt {\frac {27 \textit {\_a} \,\textit {\_f}^{2}-2 \textit {\_f}}{\textit {\_a}}}}{9}+\textit {\_f} \right )\right )^{\frac {2}{3}}+6 \textit {\_a} \textit {\_f} \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0\]