\[ \boxed { \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 1.083138 (sec), leaf count = 371 \[ \left \{\left \{y(x)\to c_2 \exp \left (\frac {1}{12} \left (-2 \sqrt {3} \tan ^{-1}\left (\frac {1+2 \text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^2}{\sqrt {3}}\right )-3 \log \left (\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^4+\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^2+1\right )\right )\right )\right \}\right \} \]
Maple: cpu = 0.842 (sec), leaf count = 295 \[ \left \{ y \left ( x \right ) ={{\it \_C2} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{-{\frac {{{\it \_C1}}^{2}}{ 4\,{{\it \_C1}}^{2}+4}}} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {{{\it \_C1}}^{2}}{2\,{{\it \_C1}}^{2}+2}}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{-{\frac {1}{4\,{{\it \_C1}}^{2}+4}}} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {1}{2\,{{\it \_C1}}^{2}+2 }}} \left ( {{\rm e}^{\int \!{\frac {1}{2\,{\it \_C1}+2\,\tan \left ( \sqrt {3}x \right ) }\sqrt {4\,{{\it \_C1}}^{2}+2\,{\it \_C1}\,\tan \left ( \sqrt {3}x \right ) +4\, \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+3\,{{\it \_C1}}^{2} \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+3}}\,{\rm d}x}} \right ) ^{-1}},y \left ( x \right ) = \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{ 2} \right ) ^{-{\frac {{{\it \_C1}}^{2}}{4\,{{\it \_C1}}^{2}+4}}} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {{ {\it \_C1}}^{2}}{2\,{{\it \_C1}}^{2}+2}}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{-{\frac {1}{4\,{{ \it \_C1}}^{2}+4}}} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {1}{2\,{{\it \_C1}}^{2}+2}}}{{\rm e}^{\int \!{\frac {1}{2\,{\it \_C1}+2\,\tan \left ( \sqrt {3}x \right ) }\sqrt {4\,{{\it \_C1}}^{2}+2\,{\it \_C1}\,\tan \left ( \sqrt {3}x \right ) +4\, \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+3\,{{\it \_C1}}^{2} \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+3}}\,{\rm d}x}}{ \it \_C2} \right \} \]