\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-3 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{2/3} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+9 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{5/3}=0 \] ✓ Mathematica : cpu = 0.790217 (sec), leaf count = 258
\[\left \{\text {Solve}\left [-\frac {\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right )^{3/2} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2 \log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))}{6 \left (\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right ) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{4/3}\right )^{3/2}}+\frac {\sqrt {\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right ) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{4/3}} \log \left (\sqrt {\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}+\text {Global$\grave { }$x}\right )}{\sqrt {\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{2/3}}+\frac {1}{6} \log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ],\text {Solve}\left [\frac {1}{6} \left (\frac {\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right )^{3/2} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2 \log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))}{\left (\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right ) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{4/3}\right )^{3/2}}+\log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))\right )-\frac {\sqrt {\left (\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right ) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{4/3}} \log \left (\sqrt {\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}+\text {Global$\grave { }$x}\right )}{\sqrt {\text {Global$\grave { }$x}^2-4 \sqrt [3]{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{2/3}}=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\right \}\]
✓ Maple : cpu = 2.574 (sec), leaf count = 137
\[ \left \{ \ln \left ( x \right ) -{\frac {1}{6}\ln \left ( 4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}-1 \right ) }+{\frac {1}{6}\ln \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) }+{1\sqrt {-4\, \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{5/3}+ \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{{\frac {4}{3}}}}{\it Artanh} \left ( \sqrt {-4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1} \right ) \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{-{\frac {2}{3}}}{\frac {1}{\sqrt {-4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1}}}}-{\frac {1}{6}\ln \left ( 16\, \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{2/3}+4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1 \right ) }+{\frac {1}{6}\ln \left ( 64\,{\frac {y \left ( x \right ) }{{x}^{6}}}-1 \right ) }-{\it \_C1}=0,y \left ( x \right ) ={\frac {{x}^{6}}{64}} \right \} \]