\[ a y(x)+y''(x)+y(x) y'(x)-y(x)^3=0 \] ✓ Mathematica : cpu = 9.43759 (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 = 1.922 (sec), leaf count = 1088
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{-63\,{{\it \_a}}^{2}+63\,a} \left ( {\frac { \left ( {\frac {i}{2}}\sqrt {3}-{\frac {1}{2}} \right ) ^{3}}{2} \left ( 126\,{\frac {1}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}}}-126\,{({{\it \_a}}^{6}-3\,a{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}{a}^{2}-{a}^{3}){\frac {1}{\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}}}}}-126 \right ) }+63 \right ) }{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{\frac {1}{ \left ( -{{\it \_a}}^{2}+a \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) } \left ( { \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) \left ( -{{\it \_a}}^{2}+a \right ) ^{3}{\frac {1}{\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}}}}}+\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}} \right ) }{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{\frac {1}{ \left ( -2\,{{\it \_a}}^{2}+2\,a \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) } \left ( { \left ( i\sqrt {3}-1 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) \left ( -{{\it \_a}}^{2}+a \right ) ^{3}{\frac {1}{\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}}}}}+ \left ( -i\sqrt {3}-1 \right ) \sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}} \right ) }{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{\frac {1}{ \left ( -2\,{{\it \_a}}^{2}+2\,a \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) } \left ( -{ \left ( i\sqrt {3}+1 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) \left ( -{{\it \_a}}^{2}+a \right ) ^{3}{\frac {1}{\sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}}}}}+ \left ( i\sqrt {3}-1 \right ) \sqrt [3]{-4\, \left ( {\it \_C1}\,\sqrt {5}\sqrt {{\frac {{\it \_C1}}{-{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3}}}}+1/4 \right ) \left ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) ^{2} \left ( -{{\it \_a}}^{2}+a \right ) ^{3}} \right ) }{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]