\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$x}=0 \] ✓ Mathematica : cpu = 0.526736 (sec), leaf count = 166
\[\left \{\text {Solve}\left [\frac {\left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}-1\right ) \left (\left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}-1\right ) \log \left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}-1\right )-1\right )}{\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}-\frac {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}}=c_1+\log (\text {Global$\grave { }$x}),\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ],\text {Solve}\left [\frac {\left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}+1\right ) \left (\left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}+1\right ) \log \left (\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}+1\right )+1\right )}{\frac {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+\sqrt {\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}-1}}=c_1-\log (\text {Global$\grave { }$x}),\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\right \}\]
✓ Maple : cpu = 0.052 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) = \left ( {\frac {1}{2} \left ( {\it lambertW} \left ( {\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) +1 \right ) ^{2} \left ( {\it lambertW} \left ( {\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) \right ) ^{-2}}+{\frac {1}{2}} \right ) x,y \left ( x \right ) = \left ( {\frac {1}{2} \left ( {\it lambertW} \left ( -{\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) +1 \right ) ^{2} \left ( {\it lambertW} \left ( -{\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) \right ) ^{-2}}+{\frac {1}{2}} \right ) x \right \} \]