\[ a y(x) y''(x)+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0268214 (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 = 0.856 (sec), leaf count = 129
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) ={\frac {{\it \_g} \left ( {\it \_f} \right ) \left ( 6\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{{\it \_f}}^{2}+2\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{\it \_f}\,a+7\,{\it \_g} \left ( {\it \_f} \right ) {\it \_f}+{\it \_g} \left ( {\it \_f} \right ) a+1 \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -2\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}} \right \} , \left \{ x=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{\it \_f}+{\it \_C1},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} \]