\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 0.437507 (sec), leaf count = 1757
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}+\frac {1}{4} \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}-\frac {-9 \text {Global$\grave { }$x}^4-72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}-72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}}{36 \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}-\frac {1}{8} \left (1-i \sqrt {3}\right ) \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}+\frac {\left (1+i \sqrt {3}\right ) \left (-9 \text {Global$\grave { }$x}^4-72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}-72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}\right )}{72 \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}-\frac {1}{8} \left (1+i \sqrt {3}\right ) \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}+\frac {\left (1-i \sqrt {3}\right ) \left (-9 \text {Global$\grave { }$x}^4-72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}-72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}\right )}{72 \sqrt [3]{\text {Global$\grave { }$x}^6-20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {-\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9-\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6-3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3-3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}+\frac {1}{4} \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}-\frac {-9 \text {Global$\grave { }$x}^4+72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}+72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}}{36 \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}-\frac {1}{8} \left (1-i \sqrt {3}\right ) \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}+\frac {\left (1+i \sqrt {3}\right ) \left (-9 \text {Global$\grave { }$x}^4+72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}+72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}\right )}{72 \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\text {Global$\grave { }$x}^2}{4}-\frac {1}{8} \left (1+i \sqrt {3}\right ) \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}+\frac {\left (1-i \sqrt {3}\right ) \left (-9 \text {Global$\grave { }$x}^4+72 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}+72 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}\right )}{72 \sqrt [3]{\text {Global$\grave { }$x}^6+20 \cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^3+20 \sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^3-8 \cosh \left (6 c_1\right )-8 \sinh \left (6 c_1\right )+8 \sqrt {\cosh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+\sinh \left (3 c_1\right ) \text {Global$\grave { }$x}^9+3 \cosh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \sinh \left (6 c_1\right ) \text {Global$\grave { }$x}^6+3 \cosh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+3 \sinh \left (9 c_1\right ) \text {Global$\grave { }$x}^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )}}}\right \}\right \}\]
✓ Maple : cpu = 0.652 (sec), leaf count = 656
\[ \left \{ y \left ( x \right ) =- \left ( {\frac {1}{2}\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}+{\frac {{x}^{2}}{2}{\frac {1}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}}+{\frac {x}{2}} \right ) ^{2}+2\,x \left ( 1/2\,\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}+1/2\,{\frac {{x}^{2}}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}+x/2 \right ) ,y \left ( x \right ) =- \left ( -{\frac {1}{4}\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}-{\frac {{x}^{2}}{4}{\frac {1}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}}+{\frac {x}{2}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2}\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}-{\frac {{x}^{2}}{2}{\frac {1}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}+2\,x \left ( -1/4\,\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}-1/4\,{\frac {{x}^{2}}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}+x/2-i/2\sqrt {3} \left ( 1/2\,\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}-1/2\,{\frac {{x}^{2}}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}} \right ) \right ) ,y \left ( x \right ) =- \left ( -{\frac {1}{4}\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}-{\frac {{x}^{2}}{4}{\frac {1}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}}+{\frac {x}{2}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2}\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}-{\frac {{x}^{2}}{2}{\frac {1}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}+2\,x \left ( -1/4\,\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}-1/4\,{\frac {{x}^{2}}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}}+x/2+i/2\sqrt {3} \left ( 1/2\,\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}-1/2\,{\frac {{x}^{2}}{\sqrt [3]{-6\,{\it \_C1}+{x}^{3}+2\,\sqrt {-3\,{x}^{3}{\it \_C1}+9\,{{\it \_C1}}^{2}}}}} \right ) \right ) \right \} \]