\[ 3 y'(x)^2-2 x y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.330346 (sec), leaf count = 1093
\[\left \{\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+3 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-24 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+243 e^{12 c_1}+48 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,6\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 x^2+3 e^{12 c_1}+3888 \text {$\#$1}^6+216 e^{6 c_1} \text {$\#$1}^3\& ,5\right ]\right \},\left \{y(x)\to \text {Root}\left [-16 e^{6 c_1} x^6+243 \text {$\#$1}^4 x^4+144 e^{6 c_1} \text {$\#$1} x^4-1944 \text {$\#$1}^5 x^2-378 e^{6 c_1} \text {$\#$1}^2 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 = 0.044 (sec), leaf count = 580
\[\left \{y \left (x \right ) = -\frac {\left (-i \sqrt {3}\, x^{2}-x^{2}+2 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}} x +i \sqrt {3}\, \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}-\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}\right ) \left (-i \sqrt {3}\, x^{2}-x^{2}-6 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}} x +i \sqrt {3}\, \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}-\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}\right )}{48 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}}, y \left (x \right ) = -\frac {\left (-i \sqrt {3}\, x^{2}+x^{2}-2 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}} x +i \sqrt {3}\, \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}+\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}\right ) \left (-i \sqrt {3}\, x^{2}+x^{2}+6 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}} x +i \sqrt {3}\, \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}+\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}\right )}{48 \left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {2}{3}}}, y \left (x \right ) = \frac {\left (\frac {x^{2}}{\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}}}+x +\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}}\right ) x}{3}-\frac {\left (\frac {x^{2}}{\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}}}+x +\left (x^{3}-54 c_{1}+6 \sqrt {-3 c_{1} x^{3}+81 c_{1}^{2}}\right )^{\frac {1}{3}}\right )^{2}}{12}\right \}\]