\[ y''(x)+y(x) y'(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 2.8407 (sec), leaf count = 492
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {2}{\frac {e^{6 c_1} K[1]^4}{\sqrt [3]{e^{18 c_1} K[1]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[1]^6}}}-K[1]^2+e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[1]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[1]^6}}}dK[1]\& \right ][c_2+x]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-\frac {\left (1+i \sqrt {3}\right ) e^{6 c_1} K[2]^4}{4 \sqrt [3]{e^{18 c_1} K[2]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[2]^6}}}-\frac {K[2]^2}{2}-\frac {1}{4} \left (1-i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[2]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[2]^6}}}dK[2]\& \right ][c_2+x]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-\frac {\left (1-i \sqrt {3}\right ) e^{6 c_1} K[3]^4}{4 \sqrt [3]{e^{18 c_1} K[3]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[3]^6}}}-\frac {K[3]^2}{2}-\frac {1}{4} \left (1+i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[3]^6-2 e^{12 c_1}+2 \sqrt {e^{24 c_1}-e^{30 c_1} K[3]^6}}}dK[3]\& \right ][c_2+x]\right \}\right \}\] ✓ Maple : cpu = 0.086 (sec), leaf count = 253
\[ \left \{ \int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}-{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}-{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}+{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]