\[ \boxed { x \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{2}-{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.552570 (sec), leaf count = 1921 \[ \left \{\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,7\right ]\right \},\left \{y(x)\to \text {Root}\left [1024 x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+81 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4 e^{24 c_1} \text {$\#$1}^6\& ,8\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,7\right ]\right \},\left \{y(x)\to \text {Root}\left [x^{12}-576 e^{12 c_1} \text {$\#$1}^4 x^8-2176 e^{12 c_1} \text {$\#$1}^3 x^6+82944 e^{24 c_1} \text {$\#$1}^8 x^4-1536 e^{12 c_1} \text {$\#$1}^2 x^4+36864 e^{24 c_1} \text {$\#$1}^7 x^2-384 e^{12 c_1} \text {$\#$1} x^2-32 e^{12 c_1}+4096 e^{24 c_1} \text {$\#$1}^6\& ,8\right ]\right \}\right \} \]
Maple: cpu = 1.638 (sec), leaf count = 221 \[ \left \{ y \left ( x \right ) =-{\frac {2}{9\,{x}^{2}}},y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( -729\,{\it \_C1}\,{x}^{ 12}+{{\it \_Z}}^{8}-12\,{{\it \_Z}}^{7}+60\,{{\it \_Z}}^{6}-160\,{{ \it \_Z}}^{5}+240\,{{\it \_Z}}^{4}-192\,{{\it \_Z}}^{3}+64\,{{\it \_Z} }^{2} \right ) -2 \right ) \left ( {\it RootOf} \left ( -729\,{\it \_C1} \,{x}^{12}+{{\it \_Z}}^{8}-12\,{{\it \_Z}}^{7}+60\,{{\it \_Z}}^{6}-160 \,{{\it \_Z}}^{5}+240\,{{\it \_Z}}^{4}-192\,{{\it \_Z}}^{3}+64\,{{\it \_Z}}^{2} \right ) +1 \right ) }{9\,{x}^{2}}},y \left ( x \right ) ={ \frac { \left ( {\it RootOf} \left ( -729\,{x}^{12}+{\it \_C1}\,{{\it \_Z}}^{8}+4\,{\it \_C1}\,{{\it \_Z}}^{7}+4\,{\it \_C1}\,{{\it \_Z}}^{6 }-4\,{\it \_C1}\,{{\it \_Z}}^{5}-10\,{\it \_C1}\,{{\it \_Z}}^{4}-4\,{ \it \_C1}\,{{\it \_Z}}^{3}+4\,{{\it \_Z}}^{2}{\it \_C1}+4\,{\it \_C1} \,{\it \_Z}+{\it \_C1} \right ) -2 \right ) \left ( {\it RootOf} \left ( -729\,{x}^{12}+{\it \_C1}\,{{\it \_Z}}^{8}+4\,{\it \_C1}\,{{\it \_Z}}^ {7}+4\,{\it \_C1}\,{{\it \_Z}}^{6}-4\,{\it \_C1}\,{{\it \_Z}}^{5}-10\, {\it \_C1}\,{{\it \_Z}}^{4}-4\,{\it \_C1}\,{{\it \_Z}}^{3}+4\,{{\it \_Z}}^{2}{\it \_C1}+4\,{\it \_C1}\,{\it \_Z}+{\it \_C1} \right ) +1 \right ) }{9\,{x}^{2}}} \right \} \]