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 = 0.408235 (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 = 1.021 (sec), leaf count = 67
\[\left [y \left (x \right ) = \int \RootOf \left (3 \left (\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {6 \textit {\_f}^{3}+9 \textit {\_f}^{2}+9 \textit {\_C1}}}d \textit {\_f} \right )+x +\textit {\_C2} \right )d x +\textit {\_C3}, y \left (x \right ) = \int \RootOf \left (-3 \left (\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {6 \textit {\_f}^{3}+9 \textit {\_f}^{2}+9 \textit {\_C1}}}d \textit {\_f} \right )+x +\textit {\_C2} \right )d x +\textit {\_C3}\right ]\] 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))
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]