\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2+\text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 0.549525 (sec), leaf count = 181
\[\left \{\text {Solve}\left [\frac {\left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}-1\right ) \left (\left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}-1\right ) \log \left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}-1\right )-1\right )}{2 \left (-\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}-1\right )}=c_1+\frac {\log (\text {Global$\grave { }$x})}{2},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ],\text {Solve}\left [\frac {\left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}+1\right ) \left (\left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}+1\right ) \log \left (\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}+1\right )+1\right )}{2 \left (\frac {2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+\sqrt {\frac {4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})}{\text {Global$\grave { }$x}}+1}+1\right )}=c_1-\frac {\log (\text {Global$\grave { }$x})}{2},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\right \}\]
✓ Maple : cpu = 0.041 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) = \left ( {\frac {1}{4} \left ( {\it lambertW} \left ( -{\frac {1}{2}{\frac {1}{\sqrt {{\frac {{\it \_C1}}{x}}}}}} \right ) \right ) ^{-2}}+{\frac {1}{2} \left ( {\it lambertW} \left ( -{\frac {1}{2}{\frac {1}{\sqrt {{\frac {{\it \_C1}}{x}}}}}} \right ) \right ) ^{-1}} \right ) x,y \left ( x \right ) = \left ( {\frac {1}{4} \left ( {\it lambertW} \left ( {\frac {1}{2}{\frac {1}{\sqrt {{\frac {{\it \_C1}}{x}}}}}} \right ) \right ) ^{-2}}+{\frac {1}{2} \left ( {\it lambertW} \left ( {\frac {1}{2}{\frac {1}{\sqrt {{\frac {{\it \_C1}}{x}}}}}} \right ) \right ) ^{-1}} \right ) x \right \} \]