\[ 3 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 0.335594 (sec), leaf count = 1093
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,1\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,2\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,3\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,4\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,5\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+3 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-24 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,6\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,1\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,2\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,3\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,4\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,5\right ]\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {Root}\left [-16 e^{6 c_1} \text {Global$\grave { }$x}^6+243 \text {$\#$1}^4 \text {Global$\grave { }$x}^4+144 e^{6 c_1} \text {$\#$1} \text {Global$\grave { }$x}^4-1944 \text {$\#$1}^5 \text {Global$\grave { }$x}^2-378 e^{6 c_1} \text {$\#$1}^2 \text {Global$\grave { }$x}^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,6\right ]\right \}\right \}\]
✓ Maple : cpu = 0.032 (sec), leaf count = 656
\[ \left \{ y \left ( x \right ) =-3\, \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}+1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6 \right ) ^{2}+2\,x \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}+1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6 \right ) ,y \left ( x \right ) =-3\, \left ( -1/12\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/12\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6-i/2\sqrt {3} \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}} \right ) \right ) ^{2}+2\,x \left ( -1/12\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/12\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6-i/2\sqrt {3} \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}} \right ) \right ) ,y \left ( x \right ) =-3\, \left ( -1/12\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/12\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6+i/2\sqrt {3} \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}} \right ) \right ) ^{2}+2\,x \left ( -1/12\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/12\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}}+x/6+i/2\sqrt {3} \left ( 1/6\,\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}-1/6\,{\frac {{x}^{2}}{\sqrt [3]{-54\,{\it \_C1}+{x}^{3}+6\,\sqrt {-3\,{x}^{3}{\it \_C1}+81\,{{\it \_C1}}^{2}}}}} \right ) \right ) \right \} \]