\[ \boxed { {x}^{4}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 0.642582 (sec), leaf count = 329 \[ \left \{\left \{y(x)\to -i x \log \left (-\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}}{4 c_1 x}-\frac {i \sinh \left (c_2\right )}{4 c_1 x}-\frac {i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (-\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}}{4 c_1 x}+\frac {i \sinh \left (c_2\right )}{4 c_1 x}+\frac {i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}}{4 c_1 x}-\frac {i \sinh \left (c_2\right )}{4 c_1 x}-\frac {i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\sqrt {-8 i c_1 x^2-\sinh \left (2 c_2\right )-\cosh \left (2 c_2\right )}}{4 c_1 x}+\frac {i \sinh \left (c_2\right )}{4 c_1 x}+\frac {i \cosh \left (c_2\right )}{4 c_1 x}\right )\right \}\right \} \]
Maple: cpu = 1.623 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) = \left ( -\arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2}-1}}} \right ) +{\it \_C2} \right ) x,y \left ( x \right ) = \left ( \arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2} -1}}} \right ) +{\it \_C2} \right ) x \right \} \]