ODE
\[ y'''(x)+y'(x)^2-y(x) y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0349194 (sec), leaf count = 0 , could not solve
DSolve[-(y[x]*Derivative[1][y][x]) + Derivative[1][y][x]^2 + Derivative[3][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.373 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ -{\it \_b} \left ( {\it \_a} \right ) \left ( - \left ( {\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) - \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_a}-{\it \_b} \left ( {\it \_a} \right ) \right ) =0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[-(y[x]*y'[x]) + y'[x]^2 + y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[-(y[x]*Derivative[1][y][x]) + Derivative[1][y][x]^2 + Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-y(x)*diff(y(x),x)+diff(y(x),x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a,[{-_b(_a)*(-diff(diff(_b(_a),_a),_a)*_b(_a)-diff(_b(_a),_a)^2+_a-_b(_a)) = 0}, {_a = y(x), _b(_a) = diff(y(x),x)}, {x = Int(1/_b(_a),_a)+_C1, y(x) = _a}])