\[ 3 x^2 y''(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)+4 y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0047277 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_1{}^2 x^2}{c_2}+c_1 x+c_2\right \}\right \}\] ✓ Maple : cpu = 2.731 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={x}^{{\frac {2\,\sqrt {3}}{3}}}{\it \_C1}\,x,y \left ( x \right ) ={\frac {{{\it \_C1}}^{2}{x}^{2}}{{\it \_C2}}}+{\it \_C1}\,x+{\it \_C2} \right \} \]