\[ a y(x)+y(x) y'(x)+y''(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 8.61172 (sec), leaf count = 990
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\frac {e^{6 c_1} \left (a-K[1]^2\right )^2}{2 \sqrt [3]{e^{18 c_1} K[1]^6-3 a e^{18 c_1} K[1]^4+3 a^2 e^{18 c_1} K[1]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[1]^6+3 a e^{30 c_1} K[1]^4-3 a^2 e^{30 c_1} K[1]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}+\frac {1}{2} \left (a-K[1]^2\right )+\frac {1}{2} e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[1]^6-3 a e^{18 c_1} K[1]^4+3 a^2 e^{18 c_1} K[1]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[1]^6+3 a e^{30 c_1} K[1]^4-3 a^2 e^{30 c_1} K[1]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}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} \left (a-K[2]^2\right )^2}{4 \sqrt [3]{e^{18 c_1} K[2]^6-3 a e^{18 c_1} K[2]^4+3 a^2 e^{18 c_1} K[2]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[2]^6+3 a e^{30 c_1} K[2]^4-3 a^2 e^{30 c_1} K[2]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}+\frac {1}{2} \left (a-K[2]^2\right )-\frac {1}{4} \left (1-i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[2]^6-3 a e^{18 c_1} K[2]^4+3 a^2 e^{18 c_1} K[2]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[2]^6+3 a e^{30 c_1} K[2]^4-3 a^2 e^{30 c_1} K[2]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}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} \left (a-K[3]^2\right )^2}{4 \sqrt [3]{e^{18 c_1} K[3]^6-3 a e^{18 c_1} K[3]^4+3 a^2 e^{18 c_1} K[3]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[3]^6+3 a e^{30 c_1} K[3]^4-3 a^2 e^{30 c_1} K[3]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}+\frac {1}{2} \left (a-K[3]^2\right )-\frac {1}{4} \left (1+i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{e^{18 c_1} K[3]^6-3 a e^{18 c_1} K[3]^4+3 a^2 e^{18 c_1} K[3]^2-2 e^{12 c_1}-a^3 e^{18 c_1}+2 \sqrt {-e^{30 c_1} K[3]^6+3 a e^{30 c_1} K[3]^4-3 a^2 e^{30 c_1} K[3]^2+e^{24 c_1}+a^3 e^{30 c_1}}}}dK[3]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 3.976 (sec), leaf count = 108
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {4\, \left ( {\it RootOf} \left ( \left ( -4\,{{\it \_a}}^{6}+12\,{{\it \_a}}^{4}a-12\,{{\it \_a}}^{2}{a}^{2}+4\,{a}^{3}+320\,{\it \_C1} \right ) {{\it \_Z}}^{9}+ \left ( -189\,{{\it \_a}}^{6}+567\,{{\it \_a}}^{4}a-567\,{{\it \_a}}^{2}{a}^{2}+189\,{a}^{3}+15120\,{\it \_C1} \right ) {{\it \_Z}}^{6}+238140\,{\it \_C1}\,{{\it \_Z}}^{3}+1250235\,{\it \_C1} \right ) \right ) ^{3}+63}{-63\,{{\it \_a}}^{2}+63\,a}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]