\[ x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0 \] ✓ Mathematica : cpu = 36.6769 (sec), leaf count = 248
\[\text {Solve}\left [-\int _1^{\frac {y(x)}{x}}\frac {i \sqrt {3} \sqrt {K[2]} J_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right )+\sqrt {K[2]} J_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right )-2 J_{1+i \sqrt {3}}\left (2 \sqrt {K[2]}\right ) K[2]-2 Y_{1+i \sqrt {3}}\left (2 \sqrt {K[2]}\right ) c_1 K[2]+i \sqrt {3} Y_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right ) c_1 \sqrt {K[2]}+Y_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right ) c_1 \sqrt {K[2]}}{\left (J_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right )+Y_{i \sqrt {3}}\left (2 \sqrt {K[2]}\right ) c_1\right ) K[2]^{3/2}}dK[2]-2 \log (x)+2 c_2=0,y(x)\right ]\] ✓ Maple : cpu = 1.401 (sec), leaf count = 166
\[\left \{y \left (x \right ) = x \RootOf \left (2 c_{2}-\left (\int _{}^{\textit {\_Z}}\frac {-2 c_{1} \textit {\_f} \BesselY \left (1+i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )+i c_{1} \sqrt {3}\, \sqrt {\textit {\_f}}\, \BesselY \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )+c_{1} \sqrt {\textit {\_f}}\, \BesselY \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )-2 \textit {\_f} \BesselJ \left (1+i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )+i \sqrt {3}\, \sqrt {\textit {\_f}}\, \BesselJ \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )+\sqrt {\textit {\_f}}\, \BesselJ \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )}{\left (c_{1} \BesselY \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )+\BesselJ \left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )\right ) \textit {\_f}^{\frac {3}{2}}}d \textit {\_f} \right )-2 \ln \left (x \right )\right )\right \}\]