\[ -2 \text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+2 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2+3 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 2865.29 (sec), leaf count = 290
\[\left \{\text {Solve}\left [\frac {1}{3} \left (\log \left (\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right )-\log \left (6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-\text {Global$\grave { }$x}^3\right )+\log \left (6-\text {Global$\grave { }$x}^3\right )-\log \left (3 \left (\text {Global$\grave { }$x}^3-6\right )\right )-\frac {\sqrt {\text {Global$\grave { }$x}^4-6 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})} \log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))}{\sqrt {\text {Global$\grave { }$x}} \sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}+\log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))+\log (3)\right )+\frac {2 \sqrt {\text {Global$\grave { }$x}^4-6 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})} \log \left (\text {Global$\grave { }$x}^{3/2}+\sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right )}{3 \sqrt {\text {Global$\grave { }$x}} \sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ],\text {Solve}\left [\frac {1}{3} \left (\log \left (\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right )-\log \left (6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-\text {Global$\grave { }$x}^3\right )+\log \left (6-\text {Global$\grave { }$x}^3\right )-\log \left (3 \left (\text {Global$\grave { }$x}^3-6\right )\right )+\frac {\sqrt {\text {Global$\grave { }$x}^4-6 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})} \log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))}{\sqrt {\text {Global$\grave { }$x}} \sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}+\log (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))+\log (3)\right )-\frac {2 \sqrt {\text {Global$\grave { }$x}^4-6 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})} \log \left (\text {Global$\grave { }$x}^{3/2}+\sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}\right )}{3 \sqrt {\text {Global$\grave { }$x}} \sqrt {\text {Global$\grave { }$x}^3-6 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}}=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\right \}\]
✓ Maple : cpu = 0.19 (sec), leaf count = 117
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}}{6}},y \left ( x \right ) ={\frac {1}{3\,{\it \_C1}} \left ( {x}^{3}{\it \_C1}+x \left ( -{x}^{2}{\it \_C1}+\sqrt {-6\,{\it \_C1}\,x} \right ) +3 \right ) },y \left ( x \right ) ={\frac {1}{3\,{\it \_C1}} \left ( {x}^{3}{\it \_C1}-x \left ( {x}^{2}{\it \_C1}+\sqrt {-6\,{\it \_C1}\,x} \right ) +3 \right ) },y \left ( x \right ) ={\frac {{x}^{3}}{3}}-{\frac {x}{3} \left ( {x}^{2}-\sqrt {-6\,{\it \_C1}\,x} \right ) }+{\it \_C1},y \left ( x \right ) ={\frac {{x}^{3}}{3}}-{\frac {x}{3} \left ( {x}^{2}+\sqrt {-6\,{\it \_C1}\,x} \right ) }+{\it \_C1} \right \} \]