\[ \boxed { y \left ( x \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 2.969877 (sec), leaf count = 409 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 i \sqrt {\frac {\text {$\#$1}^2}{2 \left (\sqrt {c_2^2-c_1}-c_2\right )}+1} \sqrt {1-\frac {\text {$\#$1}^2}{2 \left (c_2+\sqrt {c_2^2-c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {1}{\sqrt {c_2^2-c_1}-c_2}} \text {$\#$1}}{\sqrt {2}}\right )|\frac {c_2-\sqrt {c_2^2-c_1}}{c_2+\sqrt {c_2^2-c_1}}\right )}{\sqrt {\frac {1}{\sqrt {c_2^2-c_1}-c_2}} \sqrt {-\frac {\text {$\#$1}^4}{2}+2 \text {$\#$1}^2 c_2-2 c_1}}\& \right ]\left [c_3+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 i \sqrt {\frac {\text {$\#$1}^2}{2 \left (\sqrt {c_2^2-c_1}-c_2\right )}+1} \sqrt {1-\frac {\text {$\#$1}^2}{2 \left (c_2+\sqrt {c_2^2-c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {1}{\sqrt {c_2^2-c_1}-c_2}} \text {$\#$1}}{\sqrt {2}}\right )|\frac {c_2-\sqrt {c_2^2-c_1}}{c_2+\sqrt {c_2^2-c_1}}\right )}{\sqrt {\frac {1}{\sqrt {c_2^2-c_1}-c_2}} \sqrt {-\frac {\text {$\#$1}^4}{2}+2 \text {$\#$1}^2 c_2-2 c_1}}\& \right ]\left [c_3+x\right ]\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 77 \[ \left \{ \int ^{y \left ( x \right ) }\!-2\,{\frac {1}{\sqrt {-{{\it \_a }}^{4}+4\,{\it \_C2}\,{{\it \_a}}^{2}-4\,{{\it \_C2}}^{2}+4\,{\it \_C1 }}}}{d{\it \_a}}-x-{\it \_C3}=0,\int ^{y \left ( x \right ) }\!2\,{ \frac {1}{\sqrt {-{{\it \_a}}^{4}+4\,{\it \_C2}\,{{\it \_a}}^{2}-4\,{{ \it \_C2}}^{2}+4\,{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C3}=0 \right \} \]