ODE
\[ y'''(x)+a y(x) y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0388649 (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 = 1.77 (sec), leaf count = 129
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) ={\frac {{\it \_g} \left ( {\it \_f} \right ) \left ( 6\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{{\it \_f}}^{2}+2\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{\it \_f}\,a+7\,{\it \_g} \left ( {\it \_f} \right ) {\it \_f}+{\it \_g} \left ( {\it \_f} \right ) a+1 \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}} \right \} , \left \{ x=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{\it \_f}+{\it \_C1},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[a*y[x]*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a*y[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+a*y(x)*diff(diff(y(x),x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(exp(Int(_g(_f),_f)+_C2),[{diff(_g(_f),_f) = _g(_f)*(6*_g(_f)^2*_f^2+2*_g(_f)^2*_f*a+7*_g(_f)*_f+_g(_f)*a+1)/_f}, {_f = diff(y(x),x)/y(x)^2, _g(_f) = y(x)^2*diff(y(x),x)/(y(x)*diff(diff(y(x),x),x)-2*diff(y(x),x)^2)}, {x = Int(1/_f/exp(Int(_g(_f),_f)+_C2)*_g(_f),_f)+_C1, y(x) = exp(Int(_g(_f),_f)+_C2)}])