ODE
\[ y'''(x)=y'(x) \left (y'(x)+1\right ) \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
Book solution method
TO DO
Mathematica ✗
cpu = 1.25765 (sec), leaf count = 0 , could not solve
DSolve[Derivative[3][y][x] == Derivative[1][y][x]*(1 + Derivative[1][y][x]), y[x], x]
Maple ✓
cpu = 2.727 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( -3\,\int ^{{\it \_Z}}\!{\frac {1}{\sqrt {6\,{{\it \_f}}^{3}+9\,{{\it \_f}}^{2}+9\,{\it \_C1}}}}{d{\it \_f}}+x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C3},y \left ( x \right ) =\int \!{\it RootOf} \left ( 3\,\int ^{{\it \_Z}}\!{\frac {1}{\sqrt {6\,{{\it \_f}}^{3}+9\,{{\it \_f}}^{2}+9\,{\it \_C1}}}}{d{\it \_f}}+x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y'''[x] == y'[x]*(1 + y'[x]),y[x],x]
Mathematica raw output
DSolve[Derivative[3][y][x] == Derivative[1][y][x]*(1 + Derivative[1][y][x]), y[x], x]
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = diff(y(x),x)*(1+diff(y(x),x)), y(x),'implicit')
Maple raw output
y(x) = Int(RootOf(3*Intat(1/(6*_f^3+9*_f^2+9*_C1)^(1/2),_f = _Z)+x+_C2),x)+_C3, y(x) = Int(RootOf(-3*Intat(1/(6*_f^3+9*_f^2+9*_C1)^(1/2),_f = _Z)+x+_C2),x)+_C3