\[ a y(x)+y''(x)+y(x) y'(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 100.131 (sec), leaf count = 0 , could not solve
DSolve[a*y[x] - y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 2.888 (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 \_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 ( {\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 ) }}-126\,{({{\it \_a}}^{6}-3\,a{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}{a}^{2}-{a}^{3}){\frac {1}{\sqrt [3]{-4\, \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 ( {\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 ) }}}}-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 \_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 ( {\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 ) }}}}+\sqrt [3]{-4\, \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 ( {\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 ) } \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 ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) \left ( i\sqrt {3}-1 \right ) \left ( -{{\it \_a}}^{2}+a \right ) ^{3}{\frac {1}{\sqrt [3]{-4\, \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 ( {\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 ( -i\sqrt {3}-1 \right ) \sqrt [3]{-4\, \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 ( {\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 ) } \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 ( -{{\it \_a}}^{6}+3\,a{{\it \_a}}^{4}-3\,{{\it \_a}}^{2}{a}^{2}+80\,{{\it \_C1}}^{3}+{a}^{3} \right ) \left ( i\sqrt {3}+1 \right ) \left ( -{{\it \_a}}^{2}+a \right ) ^{3}{\frac {1}{\sqrt [3]{-4\, \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 ( {\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 ) }}}}+\sqrt [3]{-4\, \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 ( {\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 ( i\sqrt {3}-1 \right ) \right ) }{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]