\[ \left (y'(x)^2+y(x)^2\right ) y''(x)+y(x)^3=0 \] ✓ Mathematica : cpu = 1.12368 (sec), leaf count = 369
\[\left \{\left \{y(x)\to \frac {c_2 \exp \left (-\frac {\tan ^{-1}\left (\frac {1+2 \text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^2}{\sqrt {3}}\right )}{2 \sqrt {3}}\right )}{\sqrt [4]{\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^4+\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ]\left [c_1-x\right ]{}^2+1}}\right \}\right \}\]
✓ Maple : cpu = 1.39 (sec), leaf count = 291
\[ \left \{ y \left ( x \right ) ={ \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{ \left ( 2\,{{\it \_C1}}^{2}+2 \right ) ^{-1}}{\it \_C2} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {{{\it \_C1}}^{2}}{2\,{{\it \_C1}}^{2}+2}}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{-{\frac {{{\it \_C1}}^{2}}{4\,{{\it \_C1}}^{2}+4}}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{- \left ( 4\,{{\it \_C1}}^{2}+4 \right ) ^{-1}} \left ( {{\rm e}^{\int \!{\frac {1}{2\,{\it \_C1}+2\,\tan \left ( \sqrt {3}x \right ) }\sqrt { \left ( 3\,{{\it \_C1}}^{2}+4 \right ) \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+2\,{\it \_C1}\,\tan \left ( \sqrt {3}x \right ) +4\,{{\it \_C1}}^{2}+3}}\,{\rm d}x}} \right ) ^{-1}},y \left ( x \right ) = \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{{\frac {{{\it \_C1}}^{2}}{2\,{{\it \_C1}}^{2}+2}}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{-{\frac {{{\it \_C1}}^{2}}{4\,{{\it \_C1}}^{2}+4}}} \left ( {\it \_C1}+\tan \left ( \sqrt {3}x \right ) \right ) ^{ \left ( 2\,{{\it \_C1}}^{2}+2 \right ) ^{-1}} \left ( 1+ \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2} \right ) ^{- \left ( 4\,{{\it \_C1}}^{2}+4 \right ) ^{-1}}{{\rm e}^{\int \!{\frac {1}{2\,{\it \_C1}+2\,\tan \left ( \sqrt {3}x \right ) }\sqrt { \left ( 3\,{{\it \_C1}}^{2}+4 \right ) \left ( \tan \left ( \sqrt {3}x \right ) \right ) ^{2}+2\,{\it \_C1}\,\tan \left ( \sqrt {3}x \right ) +4\,{{\it \_C1}}^{2}+3}}\,{\rm d}x}}{\it \_C2} \right \} \]