\[ \left (y'(x)^2+y(x)^2\right ) y''(x)+y(x)^3=0 \] ✓ Mathematica : cpu = 0.824806 (sec), leaf count = 371
\[\left \{\left \{y(x)\to c_2 \exp \left (\frac {1}{12} \left (-2 \sqrt {3} \tan ^{-1}\left (\frac {1+2 \text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ][-x+c_1]{}^2}{\sqrt {3}}\right )-3 \log \left (\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ][-x+c_1]{}^4+\text {InverseFunction}\left [\frac {\left (\sqrt {3}-i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1-i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1-i \sqrt {3}\right )}}+\frac {\left (\sqrt {3}+i\right ) \tan ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\frac {1}{2} \left (1+i \sqrt {3}\right )}}\right )}{\sqrt {6 \left (1+i \sqrt {3}\right )}}\& \right ][-x+c_1]{}^2+1\right )\right )\right )\right \}\right \}\] ✓ Maple : cpu = 1.571 (sec), leaf count = 293
\[y \relax (x ) = \left (1+\tan ^{2}\left (\sqrt {3}\, x \right )\right )^{-\frac {c_{1}^{2}}{4 c_{1}^{2}+4}} \left (c_{1}+\tan \left (\sqrt {3}\, x \right )\right )^{\frac {c_{1}^{2}}{2 c_{1}^{2}+2}} {\mathrm e}^{\int -\frac {\sqrt {4 c_{1}^{2}+2 c_{1} \tan \left (\sqrt {3}\, x \right )+4 \left (\tan ^{2}\left (\sqrt {3}\, x \right )\right )+3 c_{1}^{2} \left (\tan ^{2}\left (\sqrt {3}\, x \right )\right )+3}}{2 \left (c_{1}+\tan \left (\sqrt {3}\, x \right )\right )}d x} \left (1+\tan ^{2}\left (\sqrt {3}\, x \right )\right )^{-\frac {1}{4 c_{1}^{2}+4}} \left (c_{1}+\tan \left (\sqrt {3}\, x \right )\right )^{\frac {1}{2 c_{1}^{2}+2}} c_{2}\]