\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-2 \text {Global$\grave { }$x}=0 \] ✓ Mathematica : cpu = 0.623781 (sec), leaf count = 53
\[\text {Solve}\left [\left \{\text {Global$\grave { }$x}=\frac {c_1 \text {K$\$$953664}}{\sqrt {\text {K$\$$953664}^2+1}}+\frac {\text {K$\$$953664} \sinh ^{-1}(\text {K$\$$953664})}{2 \sqrt {\text {K$\$$953664}^2+1}},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=\frac {\text {K$\$$953664}}{2}-\frac {\text {Global$\grave { }$x}}{\text {K$\$$953664}}\right \},\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x}),\text {K$\$$953664}\}\right ]\]
✓ Maple : cpu = 0.075 (sec), leaf count = 217
\[ \left \{ {{\it \_C1} \left ( -2\,y \left ( x \right ) +2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x-2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}+x-{\frac {1}{2} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\it Arcsinh} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x-2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}=0,{{\it \_C1} \left ( 2\,y \left ( x \right ) +2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x+2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}+x-{\frac {1}{2} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\it Arcsinh} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x+2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}=0 \right \} \]