\[ y''(x)+y(x) y'(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 2.92562 (sec), leaf count = 492
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {2}{\frac {e^{6 c_1} K[1]^4}{\sqrt [3]{e^{18 c_1} K[1]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[1]^6}}}-K[1]^2+e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[1]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[1]^6}}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-\frac {\left (1+i \sqrt {3}\right ) e^{6 c_1} K[2]^4}{4 \sqrt [3]{e^{18 c_1} K[2]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[2]^6}}}-\frac {K[2]^2}{2}-\frac {1}{4} \left (1-i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[2]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[2]^6}}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-\frac {\left (1-i \sqrt {3}\right ) e^{6 c_1} K[3]^4}{4 \sqrt [3]{e^{18 c_1} K[3]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[3]^6}}}-\frac {K[3]^2}{2}-\frac {1}{4} \left (1+i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[3]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[3]^6}}}dK[3]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.88 (sec), leaf count = 291
\[\int _{}^{y \relax (x )}\frac {2}{\frac {\textit {\_a}^{4}}{\left (\textit {\_a}^{6}+2 c_{1}+2 \sqrt {\textit {\_a}^{6} c_{1}+c_{1}^{2}}\right )^{\frac {1}{3}}}-\textit {\_a}^{2}+\left (\textit {\_a}^{6}+2 c_{1}+2 \sqrt {\textit {\_a}^{6} c_{1}+c_{1}^{2}}\right )^{\frac {1}{3}}}d \textit {\_a} -x -c_{2} = 0\]