\[ 3 x^2 y''(x)^2+4 y'(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0060491 (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 = 0.782 (sec), leaf count = 36
\[\left \{y \left (x \right ) = 0, y \left (x \right ) = c_{1} x \,x^{\frac {2 \sqrt {3}}{3}}, y \left (x \right ) = \frac {c_{1}^{2} x^{2}}{c_{2}}+c_{1} x +c_{2}\right \}\]