\[ \boxed { \left ( 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2} \right ) ^{3}+32\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) \left ( x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 0.114015 (sec), leaf count = 143 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (-\frac {8 c_1^3}{\sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 c_1^{10} c_2^{10}-64 c_1^9 c_2^9}-9 c_1^5 c_2^5}}+\frac {c_1^2}{c_2}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {27 c_1^{10} c_2^{10}-64 c_1^9 c_2^9}-9 c_1^5 c_2^5}}{3^{2/3} c_2^3}\right ) x^2+c_1 x+c_2\right \}\right \} \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]