\[ a y(x) y''(x)+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0269833 (sec), leaf count = 0 , could not solve
DSolve[a*y[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.266 (sec), leaf count = 127
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) = \left ( 6\,{\it \_f}+2\,a \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{3}+{\frac { \left ( 7\,{\it \_f}+a \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}}{{\it \_f}}}+{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) ={ \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) }{{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }}-2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{-1}} \right \} , \left \{ x=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{\it \_f}+{\it \_C1},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} \]